Evolutionary information dynamics over social networks: a review

Hangjing Zhang; Yan Chen; H. Vicky Zhao

doi:10.1108/ijcs-09-2019-0026

Evolutionary information dynamics over social networks: a review

Zhang, Hangjing; Chen, Yan; Zhao, H. Vicky 2020-03-03 00:00:00 Purpose – The purpose of this paper is to have a review on the analysis of information diffusion based on evolutionary game theory. People now get used to interact over social networks, and one of the most important functions of social networks is information sharing. Understanding the mechanisms of the information diffusion over social networks is critical to various applications including online advertisement and rumor control. Design/methodology/approach – It has been shown that the graphical evolutionary game theory (EGT) is a very efﬁcient method to study this problem. Findings – By applying EGT to information diffusion, the authors could predict every small change in the process, get the detailed dynamics and ﬁnally foretell the stable states. Originality/value – In this paper, the authors provide a general review on the evolutionary game-theoretic framework for information diffusion over social network by summarizing the results and conclusions of works using graphical EGT. Keywords Crowd behaviour analysis, Information diffusion, Evolutionary game theory Paper type Literature review 1. Introduction Nowadays, people cannot live in individual. They have to depend on their social networks more or less and interact with others. A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. Typical social network examples include Facebook/Twitter networks, hyperlink networks of websites, scientiﬁc collaboration/citation networks and Internet of Things (IoT) (Wikipedia). With the rapid development of the internet and mobile technologies, social networks are of extremely large scale, e.g. there are over 2.41 billion monthly active users and 1.59 billion daily active users worldwide on Facebook as of June © Hangjing Zhang, Yan Chen and H. Vicky Zhao. Published in International Journal of Crowd Science. Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original International Journal of Crowd publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/ Science by/4.0/legalcode pp. 45-59 Emerald Publishing Limited This work is supported by the National Key Research and Development Program of China 2398-7294 (2017YFB1400100). DOI 10.1108/IJCS-09-2019-0026 2019 (Noyes, 2019). Meanwhile, the information size on the social networks is becoming even IJCS tremendous-scale. For instance, averagely 277,777 stories are posted on Instagram, 4,500,000 4,1 videos are watched on YouTube, 511,200 tweets are sent on Twitter and 510,000 comments are posted on Facebook in every minute (Noyes, 2019; DOMO, 2019; Martin, 2019). The information disseminated over social networks is of various kinds, e.g. when a total victory happens in a sport match, some political opinions are declared by a party or politics, some deal advertisements are released, titbits or rumors about a superstar are exposed to the public. All these information would experience the process of generation, dissemination and vanishment, and the most important part is the information diffusion. One piece of information may disappear quickly after the appearing, or last for a long time and inspire a heated discussion for its value. To ﬁgure out how the information spreads over social networks, simulating the process of information diffusion or even predicting the ﬁnal destiny of a piece of new information is vital in many applications. From users’ perspective, the diffusion dynamics or the popularity of the information is determined by complicated interactions and decision-making of other users. Based on different people’s preferences, the surrounding neighbors’ actions, the reliability of the information and many other factors, users would choose to spread information accordingly. For example, when a consumer comes across an advertisement of a new product, he or she would decide whether to trust or further diffuse it according to the comments of friends, the reputation of information publisher and manufacturer, and possibly his or her initial impression. Of course if the consumer is a fan of the product, he or she tends to share this message over social networks, which tightens the connection between the consumer and the information sender. However, if the consumer isn’t interested in it at all, he or she may regard the information spreader as worthless, and thus choose to cut the connection. In practice, the mechanisms in the process of information diffusion should be explored in depth. The study of information diffusion originates from the research of computer virus/ epidemic spreading over networks (Pastor-Satorras and Vespignani, 2001). One of the earliest and prominent works about information diffusion is (Gruhl et al.,2004), which studied the dynamics of information propagation through blogspace from both macroscopic and microscopic points of views. Subsequently, there are numerous works on the information diffusion, and researchers explore the problem from different aspects and adopt multiple methods to solve it. From the view of study object, the existing works can be divided into three categories: (1) diffusion characteristics analysis; (2) diffusion dynamics analysis; and (3) diffusion stability analysis. Among the ﬁrst category, Masahiro et al. (2009) discussed how to extract the most inﬂuential nodes on a large-scale social network in (Kimura et al., 2007). Later, many methods were proposed to mine top-k inﬂuential nodes in mobile social networks, e.g. a community-based greedy algorithm in Yu et al. (2010), the Shapley value-based Inﬂuential Nodes algorithm in Narayanam and Narahari (2011) and content-based improved greedy algorithm in Shahsavari and Golpayegani (2017) which decreased the total amount of computations. Authors in Usui et al. (2013) proposed a network growth model that can produce networks that have the necessary features for analysis and also analyzed how each feature affects information diffusion. The second category focuses on analyzing the dynamic diffusion process over different kinds of networks using different mathematical models (Damon, 2010; Yagan et al.,2013). In Damon (2010), the authors studied how a social Evolutionary network affected the spread of behavior and investigated the effects of network structure on information users’ behavior diffusion. Rather than focusing on the behavior diffusion, Bakshy et al. dynamics (2012). Studied the role of social networks in general information diffusion through an experimental approach. As online social networks, e.g. Facebook and Twitter, became more and more popular, some empirical analysis were conducted using large-scale datasets, including predicting the speed and range of information diffusion on Twitter (Jiang and Scott, 2010), modeling the global inﬂuence of a node on the rate of diffusion on Memetracker (Yang and Leskovec, 2010) and illustrating the statistical mechanics of rumor spreading on Facebook (Ostilli et al.,2010). Moreover, the information diffusion on overlaying social- physical networks was analyzed in Yagan et al. (2013). The third category of information diffusion analysis focuses on the stability and consequence of information diffusion (Peng et al., 2013; Kuhnle et al., 2018). In Peng et al. (2013), the conditions for information diffusion vanishing and information diffusion being persistent in social networks were studied. Peng et al. used a mathematical model to predict the information diffusion process of multi-source news and validated its accuracy (Yuan and Ji, 2019). How to restrain the private or contaminated information diffusion was studied in Masahiro et al. (2009) and Ilyas et al. (2011) through identifying the important information links and hubs, respectively. How to maximize information diffusion through a network was discussed in Kim and Yoneki (2012) by designing effective neighbors selection strategies, whereas in Kuhnle et al. (2018), authors proposed approximation algorithms to realize the inﬂuence maximization. From the view of adopted method, works could also be classiﬁed into two categories. The ﬁrst category focuses on macro exploration, usually adopting machine learning or data mining techniques to predict the dynamics or properties of network. Among the ﬁrst category, Pinto et al. used early diffusion data to predict future diffusion (Pinto et al.,2013) while the community structure was further exploited to improve the performance of prediction of viral memes in Weng et al. (2014). Given the information diffusion data, efﬁcient algorithms were developed to infer the underlying information diffusion network in Rodriguez et al. (2014), Rodriguez et al. (2013) and Gomez Rodriguez et al. (2013). Hao et al. (2014). proposed a matrix factorization based predictive model and used gradient descent to optimize objective function (Hao et al.,2014), whereas in Alsuwaidan and Ykhlef (2017),a novel model based on a physical radiation energy transfer mechanism was proposed to predict the diffusion graph of a certain contagion. Authors in Tsai et al. (2014) studied diffusion of preference on social networks by a rank-learning based data-driven approach. Jiang et al. (2015) proposed a K-center method to realize multi-source identiﬁcation of information diffusion and the corresponding infection regions in general networks. In Chejara and WilfredGodfrey (2018), authors presented an analysis of various heuristic based inﬂuence maximization techniques and proposed a machine learning based approach to ﬁnd the spread of information in the network. A common limitation of these ML or data mining based approaches is the lack of understanding of the underlying microscopic mechanisms of the individuals’ decision-making that dominate the information diffusion process, which is the focus of the papers in the second category. The second category models the information diffusion from the microscopic aspect, emphasizing more on the decisions and motivations of individuals. Assuming each user played the best response to the population’s strategies, Morris studied the conditions for global contagion of behaviors (Morris, 2000). The authors in Lin et al. (2013) studied the problem of predicting dynamic trends according to each users’ activeness under a dynamic activeness model. Based on the correlation, Lee and Chung (2014) proposed a probabilistic model to estimate the probability of a user’s adoption of the naive Bayes classiﬁer. A game-theoretic framework for the study of competition between ﬁrms IJCS who aimed to maximize adoption of their products by consumers located in a social network 4,1 was proposed in Goyal and Kearns (2012) and Fazeli and Jadbabaie (2012). Ding et al. (2017), Jin-lou et al. (2011) and Wang et al. (2017) proposed information diffusion models to study the spreading by deﬁning different objective functions for each user and then solving the corresponding minimization or maximization problem. To fully understand the details in information diffusion and simulate the whole process including diffusion dynamics as well as the consequence of information, in recent years some researchers put forward a novel model based on graphical evolutionary game theory (EGT). Authors in Jiang et al. (2014) and Jiang et al. (2014) proposed an evolutionary game- theoretic framework to model the dynamic information diffusion process among nodes in social networks, where the authors in Jiang et al. (2014) paid more attention to the ﬁnal stable state, while in Jiang et al. (2014), the emphasis was on the evolutionary dynamics in Cao et al. (2016) then extended the analysis of the information diffusion process to the heterogeneous social networks where nodes can have different types. In these works, the model was proved to be rather effective in accuracy, with less calculation compared with ML or data mining approaches. Based on the conclusions in the evolutionary game-theoretic framework, the dynamics and stable states in the process of information diffusion could be quickly predicted, and as a result to be applied to plenty areas such as online advertisements, rumor control and network security. Therefore, in this paper, we have a review on these works that focus on information diffusion analysis based on evolutionary game-theoretic model. We summarize the system framework and key conclusions to illustrate how the graphical EGT can be used to model information diffusion. The rest of the paper is organized as follows. Section 2 introduces evolutionary game theory, describes the graphical EGT in detail and gives some basic concepts of them. The evolutionary game-theoretic system framework and analysis results of several cases are shown in Section 3 Conclusions are drawn in Section 4. 2. Graphical evolutionary game theory and the correspondence of information diﬀusion Initially, EGT is a biological concept, starting with the problem of how to explain ritualized animal behaviour in a conﬂict situation (Wikipedia), and developing to make up for traditional game theory’s defects. In classical game theory, players are required to make rational choices, which means they should carefully consider sophisticated reasonings like what they want, what their opponents want and what their opponents know and determine the optimal strategies in competitions. Evolutionary game theory, on the other hand, does not require players to act rationally and assumes very little about the reasoning processes of the players. It focuses on the process of natural selection, i.e. evolution. It deﬁnes a framework of contests, strategies and the mathematical criteria that can be used to predict the performances of competing strategies. The results of a game include the dynamics of changes in the population, the success of strategies and any equilibrium states reached. These basic elements in a game could just correspond with the things in the process of information diffusion. We could regard the whole information diffusion process as a game, for users being players, their adopted strategies being the strategies in the game, the process of information spreading being the evolution and the consequence of information (survive or vanish, and if survive, how many users accept this piece of information) being the equilibrium states. Different from methods using a large amount of data, by applying EGT to information diffusion, we could predict every small change in the process, get the detailed dynamics and ﬁnally foretell the stable states. We are able to interpret the mechanisms of how users interact with others from the view of individuals themselves instead of the whole Evolutionary network, which helps us understand the diffusion more deeply. information Due to the structure of social network with intricate connections between users, dynamics graphical presentation of the network is combined with EGT to analyze the information dissemination as it makes problem more visualized. The social network graph is shown in Figure 1. As it shows, nodes with different colors represent different kinds of users in heterogeneous social network, and edges represent the connections between users. If users are treated as homogeneous individuals, nodes with different colors are identical in the analysis. In the model, users only have two strategies: forwarding the information and not forwarding. For the center user with a certain amount of neighbors, the numbers of his neighbor nodes adopting forwarding strategy and not forwarding strategy are certainly available. For two users with the connection, by interacting with each other with their own strategies, both sides would get same instant payoff, which equals to the beneﬁtof interaction and could be obtained according to a predeﬁned payoff matrix. Based on the payoff, we could calculate the ﬁtness of every user, involving baseline ﬁtness, payoffs and selection intensity. Baseline ﬁtness represents the player’s inherent property, e.g. a user’s own interests on the released news in a social network. In this framework, the baseline ﬁtness is normalized as one. Payoffs are determined by the payoff matrix and the graph structure. As for selection intensity, it is the relative contribution of the game to ﬁtness. When selection intensity approaches zero, it indicates the limit of weak selection (Ohtsuki et al.,2007), while selection intensity approaching one denotes strong selection, where ﬁtness equals payoffs. Here the weak selection is assumed thus selection intensity is a quite small value. After introducing ﬁtness, how to update the strategy should be deﬁned. There are many strategy updating rules from the evolutionary biology ﬁeld and they are used to model the resident/mutant evolution process. According to Ohtsukia and Nowak (2006), there are three typical and prevalent strategy updating rules: birth-death (BD), death-birth (DB) and imitation (IM) (shown in Figure 2). (1) BD updating rule: a player is chosen for reproduction with the probability being proportional to ﬁtness (Birth process). Then, the chosen player’s strategy replaces one neighbor’s strategy with uniform probability (Death process). (2) DB updating rule: a random player is chosen to abandon his/her current strategy (Death process). Then, the chosen player adopts one of his/her neighbors’ strategies with the probability being proportional to their ﬁtness (Birth process). Figure 1. An illustration of the social network IJCS 4,1 Figure 2. Three different update rules, where death selections are shown in dark blue and birth selections are shown in red (3) IM updating rule: each player either adopts the strategy of one neighbor or remains his/her current strategy, with the probability being proportional to ﬁtness. From Jiang et al. (2014), we know that the analyses of these three updating rules are similar, and the results are equivalent under weak selection scenario when the network degree is sufﬁciently large. Once a new piece of information is released by a user, other users are expected to receive the information and retransmit it to more. However, whether to forward the information depends on different users’ own choices, i.e. their strategies. Therefore, by analyzing the dynamics of users’ strategies on information forwarding, we can infer how the information propagates to other users, how popular the information is, and then ﬁnally what’sthe result of the information. To get the dynamics, ﬁrstly, the global and local network states should be deﬁned: global population state p , representing the proportion of population using the strategy; global edge state p , representing the proportion of edges with speciﬁc strategies; ij and local network state p , representing the proportion of a user’s neighbors adopting ijj the strategy. Among these notations i and j indicate different strategies, and in the model they can only be Evolutionary f for forwarding and n for not. To analyze the dynamic changing along with time, we information discretize the information diffusion process into time slots. In each time slot, users are able to dynamics observe the strategies of other adjacent users in the population. Based on the observed information, in the next time slot, each user decides on whether forwarding the information by ﬁnding out which strategy can give higher ﬁtness. Thus, as the users’ strategies update slot by slot, the network state also keeps changing slot by slot. Therefore, the evolutionary dynamics are deﬁned as the variation between every two time slots. To simplify the problem, network state and dynamics that only related to the forwarding strategy are considered, so corresponding dynamics of states are as follows: population dynamics p : dynamics of global population state, illustrating the dynamics of whole network; relationship dynamics p : dynamics of global edge state, illustrating the dynamics ff of relationship among users; and inﬂuence dynamics p : dynamics of local network state, illustrating the inﬂuence of f jf one user on his/her neighbors. As the information spreading process proceeds, the whole network would gradually reach an evolutionary stable state (ESS), i.e. all players tend to adopt their optimal stable strategies (Weibull, 1997). Intuitively, when the whole population is adopting optimal strategy, a small group of invaders using any alternate strategies should have strictly lower ﬁtness than the users of the majority, and eventually die off with a high probability. The ﬁnal ESSs can be found at the stable points of different kinds of dynamics. In summary, graph structure, players, strategy, ﬁtness (payoff) and ESS are ﬁve basic elements of a graphical evolutionary game, and these elements have perfect corresponding contents in information diffusion analysis as stated above (brieﬂy shown in the Table I), which proves that EGT is a practical and effective method to analyze information diffusion. 3. Analysis framework and results of several cases Based on the deﬁnition in graphical EGT and the coherence of information diffusion over social network, the information propagation could be studied through characteristics stated before, especially the evolutionary dynamics and ESSs which are the two most important things in the evolutionary game-theoretic framework. No matter which strategy updating rule is adopted, ESS is concluded based on the analysis of evolutionary dynamics. The basic framework of analysis can be summarized as follows. Above all, to calculate each user’s ﬁtness, we need a certain amount of neighbors adopting forwarding strategy and not forwarding strategy. However, this number is not known in every time slot during Graphical EGT Social network Table I. Graph structure Social network topology Correspondence Players Users in the social network between graphical Strategy forward the information or not EGT and social Fitness Utility from forwarding or not ESS Stable information diffusion state network prediction of detailed changing process, so we have to get its distribution. On account of the IJCS assumption that the social network is large enough, it’s reasonable to treat global population 4,1 state p or local network state p as the probability of center user encountering neighbors i ijj adopting strategy i. Thus, when the total number of neighbor nodes is given, the distribution of the number of neighbor nodes adopting every strategy is available. Based on this number, predeﬁned baseline ﬁtness, payoffs and selection intensity, each user’s ﬁtness could be obtained. Then according to the strategy updating rule, the probability of a user being chosen to reproduction or updating his/her strategy is proportional to the ﬁtness in a manner. With the probability of users’ strategy changing, we can know the probability for the increase or decrease of evolutionary states, which is exactly the evolutionary dynamics that we look for. One common method to ﬁnd ESS is to set the differential of state as zero, i.e. set the evolutionary dynamics as zero. Settle the equation and then the ESS under different conditions could ﬁnally be shown. Using the derived formula of evolutionary dynamics and ﬁnal ESS, we are able to predict the evolutionary process in every time slot, and foretell the stable states of the information diffusion, e.g. how many users still forwarding this piece of message in the social network. Here we seek out several different network structures to illustrate the framework. 3.1 Analysis of homogeneous network 3.1.1 Results over uniform degree network. In the uniform scenario, the social network based on a homogenous graph with the same degree for all users is considered. In other words, in this kind of social network, there is no difference between all users and they could be regarded as a whole of one type. Meanwhile, every user has the same number of neighbor nodes. The main reason to discuss the uniform degree network is to provide more insight into the complicated problem of information diffusion, and the derivation and results (e.g. the ﬁtness calculation and dynamics derivations) of the uniform degree network analysis will be used in the non-uniform degree case. Under the weak selection, the dynamics and ESSs could be derived in a close form. According to the formula of population dynamics, it only relies on the initial population state, the values of payoff matrix and the degree of the network, regardless of the network scale information. Therefore, the population dynamics of information diffusion over uniform degree networks show the scale-free property. Moreover, the formulashows that thedynamicisanincreasingfunctioninterms of thepayoffthat both sides adopt forwarding strategy. The corresponding physical meaning is that when the higher payoff can be obtained by forwarding the information, the increasing rate will also be higher. On the other hand, if not forwarding the information can gain higher payoff, the increasing rate will be lower, which is just the reason why population dynamic is a decreasing function in terms of the payoff that both users do not forward the information. For the formula of relationship dynamics and inﬂuence dynamics, they are functions involving themselves and also the population dynamics, which are more sophisticated. Based on the evolutionary dynamics analysis, the evolutionary stable network state could be obtained by solving equations. There are three scenarios of ESSs, which are respectively one under the case of u > u > u , zero when u > u > u , and a value ff fn nn nn fn ff between zero and one under other conditions, where u represents the payoff that both sides ff forward information and u , u are deﬁned in the same way. Zero and one are two extreme fn nn stable states, representing that no user forward the information and all users forward the information, respectively. When the population state is one, it means that both users forwarding the information can gain the most payoff, while not forwarding gains the least payoff. In a social network, this is corresponding to the scenario where the released Evolutionary information is an extremely hot topic, forwarding which can attract more attentions. On the information contrary, things are just the opposite when population stable state is zero, which is dynamics corresponding to the scenario where the released information is useless or negative advertisement, forwarding which can only incur unnecessary cost. As for the third ESS that between zero and one, there are two other cases, one of which is u > u , u > u . In this fn nn fn ff case, unilateral forwarding can bring more payoff than no forwarding or both forwarding. In a social network, this case is corresponding to the scenario where both users forwarding the information can gain only limited reward but incur more cost to both of them. An example of this case can be that the information is not the mainstream topic, e.g. the news about a punk musician and is supposed to be diffused among people with similar interests. In the other case that u > u , u > u , the payoff conﬁguration is equivalent to that of the nn fn ff fn coordination game, where both players with the same actions can make more payoff than opposite actions. An example of this case can be that the information is politically sensitive and its reality is not guaranteed, forwarding which may gain attractions but also incur potential misleading cost. In Figure 3, conclusions are veriﬁed in a synthetic network which is a homogeneous uniform degree network in four different scenarios: (1) Case 1: u = 0.8 > u = 0.6 > u = 0.4; ff fn nn (2) Case 2: u = 0.8 > u = 0.6 > u = 0.4; fn ff nn (3) Case 3: u = 0.8 > u = 0.6 > u = 0.4; and fn nn ff (4) Case 4: u = 0.8 > u = 0.6 > u = 0.4. nn fn ff From Figure 3, we can see that all the simulation results are consistent with the theoretical results, which prove the correctness of the conclusions. 3.1.2 Results over non-uniform degree network. In the non-uniform scenario, social network is based on a graph whose degree exhibits a speciﬁc distribution. This distribution means that when randomly choosing one user on the network, the probability of the chosen user with speciﬁc neighbors is a speciﬁc distribution. Note that degree correlation is not taken into account, i.e. the degrees of all users are independent of each other. So when some Figure 3. Simulation results for synthetic network which is the homogeneous uniform degree network new information is released, all users update their information forwarding strategies in a IJCS spontaneous manner. The procedure and conclusions of analysis are similar to those in 4,1 uniform degree network, and the biggest difference is that probability distribution of degree is introduced so the expectation and variance appear in the formula. Results are shown in the Figure 4, in which Erd†os-Rényi random network is adopted as non-uniform degree network in the simulation. Four cases are the same as before, and the simulation results agree well with the theoretical results. In Figure 5, the comparison of proposed model and one of the existing data mining method in Leskovec et al. (2009) is exhibited. Payoff matrices are determined by estimating using the Twitter hashtag data set. The vertical axis is the dynamics, and the mention times of different hashtags per hour in the Twitter dataset are normalized within interval and denoted by solid black square. From the ﬁgure, we can see that the graphical EGT model can ﬁt the real-world information diffusion dynamics better than the data mining method in Leskovec et al. (2009), as users’ interactions and decision-making behaviors are taken into account. 3.2 Analysis of heterogeneous network 3.2.1 Results for unknown user type model. In social network, as people have different habits and interests, there may be lots of types of users, which could be modeled as a heterogeneous network. For example, if a group of people are all sports fans, they belong to the same type considering forwarding information related to sports, while some other people belong to music lovers. Therefore, the payoff matrices of a piece of information for different types are different. When users get in touch with each other at ﬁrst, they are not familiar with each other, so they may not know which type his/her neighbors belong to, corresponding to the unknown user type model. Analyzing every type of users respectively, the dynamics of population state of each type could be deduced separately. By proportional combination, we are able to get the global evolutionary dynamics. It can be observed that the dynamic of each type not only consists of itself but also the dynamics of global state, which means that nodes are affected not only by those with the same type, but also all other nodes. Similarly, by setting the dynamics as zero, Figure 4. Simulation results for Erd†os-Rényi random network which is a homogeneous non- uniform degree network Evolutionary information dynamics (a) (b) Figure 5. (c) (d) Comparison with the existing work Notes: (a) Googlewave; (b) DavidArchuleta; (c) NIN; (d) Tehran three ESSs with different payoff matrices are derived in a close form. Figure 6 shows the simulation results of unknown user type model when the payoff matrices are set ðÞ ðÞ ðÞ ðÞ ðÞ ðÞ as: u 1 ¼ 0:4; u 1 ¼ 0:6; u 1 ¼ 0:3; u 2 ¼ 0:2; u 2 ¼ 0:4; u 2 ¼ 0:5. The nn nn ff fn ff fn theoretical dynamics ﬁt the simulation dynamics well and ESSs are predicted accurately. The average relative ESS error of the heterogeneous model is 3.54 per cent. 3.2.2 Results for known user type model. Sometimes, through repeated interactions, users may somehow manage to know their neighbors’ types. For instance, when a user observes that one of his friends frequently posts news about football match, he may gradually know that this friend is a football fan. This condition could be modeled as known user type. In other words, when the center user is deciding on whether to change the strategy, he/she treats his/her neighbors in different ways for knowing their types. As a user’s type and strategy affect its neighbors’ payoffs, they may also inﬂuence the neighbors’ strategies. Thus the edge information, i.e. relationship state (global edge state) and inﬂuence state (local network state) are required to fully characterize the network state. In the ﬁnal formulation of dynamics, it could be proved that the relationship dynamics and inﬂuence dynamics change at a much faster speed than population dynamics do. This implies that we can select a time window with an appropriate length such that the population dynamics basically remain unchanged while the relationship dynamics and inﬂuence dynamics vary a lot. So we focus on a small time period where the population dynamics do not vary with time while the inﬂuence dynamics vary. Next, it is shown that in this small time period, the inﬂuence 䣉䣣䣯䣧䢢䣶䣪䣧䣱䣴䣧䣶䣫䣥䣉䣣䣯䣧䢢䣶䣪䣧䣱䣴䣧䣶䣫䣥䣉䣣䣯䣧䢢䣶䣪䣧䣱䣴䣧䣶䣫䣥䣉䣣䣯䣧䢢䣶䣪䣧䣱䣴䣧䣶䣫䣥 IJCS 4,1 Figure 6. Simulation results of the evolutionary dynamics for the unknown user type model dynamics will converge to the corresponding population dynamics. Simulation results in Figure 7 demonstrate that the known user type model based theoretical dynamics and the simulated dynamics match well. In Figure 7, the evolutionary dynamics given by the theory of the unknown user type model are also plotted. This does not match the simulated evolutionary dynamics under the known user type model, indicating the necessity for the theory of the known user type model. 4. Conclusions In this paper, we summarize the results from works that analyze information diffusion process based on graphical evolutionary game theory over social network. To ﬁgure out the features in the process, evolutionary dynamics and evolutionary stable state are discussed. And it is found that the analysis of information diffusion based on graphical EGT matches well with reality. In the future, social network with irrational users or malicious users should also be considered, which would be more complicated compared with networks only consist of rational users. How to model the behaviours of irrational users is the focus of future research. Figure 7. Simulation of evolutionary dynamics: the known user type model References Evolutionary Alsuwaidan, L. and Ykhlef, M. (2017), “Information diffusion predictive model using radiation information transfer”, IEEE Access, Vol. 5, pp. 25946-25957. dynamics Bakshy, E., Rosenn, I., Marlow, C. and Adamic, L. (2012), “The role of social networks in information diffusion”, Proc.21stInt. Conf. World Wide Web (WWW), pp. 519-528. Cao, X., Chen, Y., Jiang, C. and Ray Liu, K.J. (2016), “Evolutionary information diffusion over heterogeneous social networks”, IEEE Transactions on Signal and Information Processing over Networks, Vol. 2 No. 4, pp. 595-610. Chejara, P. and WilfredGodfrey, W. (2018), “Machine learning based method to predict inﬂuence spread”, 2018 8th International Conference on Cloud Computing, Data Science Engineering (Conﬂuence), pp. 268-273. Damon, C. (2010), “The spread of behavior in an online social network experiment”, Science, Vol. 329 No. 5996, pp. 1194-1197, available at: https://science.sciencemag.org/content/329/5996/1194 Ding, X., Wu, Z., Chen, W., Liu, Y., Xie, Y. and Cai, S. (2017), “Modeling complex social contagions in big data era”, 2017 IEEE 2nd Advanced Information Technology, Electronic and Automation Control Conference (IAEAC), pp. 830-834. DOMO (2019), “Data never sleeps 7.0”, available at: www.domo.com/learn/data-never-sleeps-7 Fazeli, A. and Jadbabaie, A. (2012), “Game theoretic analysis of a strategic model of competitive contagion and product adoption in social networks”, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), pp. 74-79. Gomez Rodriguez, M., Leskovec, J. and Schölkopf, B. (2013), “Structure and dynamics of information pathways in online media”, Proceedings of the Sixth ACM International Conference on Web Search and Data Mining, se WSDM ’13. ACM, New York, NY, pp. 23-32, doi: 10.1145/ 2433396.2433402. Goyal, S. and Kearns, M. (2012), “Competitive contagion in networks”, Proceedings of the Forty-fourth Annual ACM Symposium on Theory of Computing, se STOC ’12. ACM, New York, NY, pp. 759-774, doi: 10.1145/2213977.2214046. Gruhl, D., Guha, R., Liben-Nowell, D. and Tomkins, A. (2004), “Information diffusion through blogspace”, Proc. 13rd Int. Conf. World Wide Web (WWW), pp. 491-501. Hao, X., Sheng, G., Yu, Z., Juncen, L., Huacan, P. and Jun, G. (2014), “Predicting information diffusion via matrix factorization based model”, 2014 4th IEEE International Conference on Network Infrastructure and Digital Content, pp. 257-261. Ilyas, M.U., Shaﬁq, M.Z., Liu, A.X. and Radha, H. (2011), “A distributed and privacy preserving algorithm for identifying information hubs in social networks”, 2011 Proceedings IEEE INFOCOM, pp. 561-565. Jiang, Y. and Scott, C. (2010), “Predicting the speed, scale, and range of information diffusion in twitter”, Conference: Proceedings of the Fourth International Conference on Weblogs and Social Media, available at: www.microsoft.com/en-us/research/publication/predicting-speed-scale-range- information-diffusion-twitter/ Jiang, C., Chen, Y. and Liu, K.J.R. (2014), “Graphical evolutionary game for information diffusion over social networks”, IEEE Journal of Selected Topics in Signal Processing, Vol. 8 No. 4, pp. 524-536. Jiang, C, Chen, Y. and Liu, K.J.R. (2014), “Evolutionary dynamics of information diffusion over social networks”, IEEE Transactions on Signal Processing, Vol. 62 No. 17, pp. 4573-4586. Jiang, J., Wen, S., Yu, S., Xiang, Y. and Zhou, W. (2015), “K-center: an approach on the multi-source identiﬁcation of information diffusion”, IEEE Transactions on Information Forensics and Security, Vol. 10 No. 12, pp. 2616-2626. Jin-Lou, Z., Zhi-bin, L. and Jian-Nan, Y. (2011), “Modeling of information diffusion based on network dimension-force”, 2011 International Conference on Management Science Engineering 18th Annual Conference Proceedings, pp. 18-27. Kim, H. and Yoneki, E. (2012), “Inﬂuential neighbours selection for information diffusion in online IJCS social networks”, 2012 21st International Conference on Computer Communications and 4,1 Networks (ICCCN), pp. 1-7. Kimura, M., Saito, K. and Nakano, R. (2007), “Extracting inﬂuential nodes for information diffusion on a social network”, Prof. of AAAI Conf. Artif. Intell, pp. 1371-1376. Kuhnle, A., Alim, M.A., Li, X., Zhang, H. and Thai, M.T. (2018), “Multiplex inﬂuence maximization in online social networks with heterogeneous diffusion models”, IEEE Transactions on Computational Social Systems, Vol. 5 No. 2, pp. 418-429. Lee, J.-R. and Chung, -W. (2014), “A new correlation-based information diffusion prediction”, Proceedings of the 23rd International Conference on World Wide Web, ser. WWW ’14 Companion, ACM, New York, NY, pp. 793-798, doi: 10.1145/2567948.2579241. Leskovec, J., Backstrom, L. and Kleinberg, J. (2009), “Meme-tracking and the dynamics of the news cycle”, Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, se KDD ’09, ACM, New York, NY, pp. 497-506, doi: 10.1145/1557019.1557077. Lin, S., Kong, X. and Yu, P.S. (2013), “Predicting trends in social networks via dynamic activeness model”, Proceedings of the 22nd ACM International Conference on Conference on Information & Knowledge Management, se CIKM ’13, ACM, New York, NY, pp. 1661-1666, doi: 10.1145/ 2505515.2505607. Martin, N. (2019), “How much data is collected every minute of the day”, available at: www.forbes.com/ sites/nicolemartin1/2019/08/07/how-much-data-is-collected-every-minute-of-the-day Masahiro, K., Kazumi, S. and Hiroshi, M. (2009), “Blocking links to minimize contamination spread in a social network”, ACM Trans. Knowl. Discov. Data, Vol. 3 No. 2, pp. 9:1-9:23, doi: 10.1145/ 1514888.1514892. Morris, S. (2000), “Contagion”, Review of Economic Studies, Vol. 67 No. 1, pp. 57-78. Narayanam, R. and Narahari, Y. (2011), “A shapley value-based approach to discover inﬂuential nodes in social networks”, IEEE Transactions on Automation Science and Engineering, Vol. 8 No. 1, pp. 130-147. Noyes, D. (2019), “The top 20 valuable facebook statistics c updated september 2019”, available at: https://zephoria.com/top-15-valuable-facebook-statistics/ Ohtsukia, H. and Nowak, M.A. (2006), “The replicator equation on graphs”, Journal of Theoretical Biology, Vol. 243 No. 1, pp. 86-97. Ohtsuki, H., Nowak, M.A. and Pacheco, J.M. (2007), “Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs”, Physical Review Letters, Vol. 98 No. 10, p. 108106. Ostilli, M., Yoneki, E., Leung, I.X., Mendes, J.F., Lio, P. and Crowcroft, J. (2010), “Statistical mechanics of rumor spreading in network communities”, Proc. Int. Conf. Comput. Sci., pp. 2331-2339. Pastor-Satorras, R. and Vespignani, A. (2001), “Epidemic spreading in scale-free networks”, Physical Review Letters, Vol. 86 No. 14, pp. 3200-3203. Peng, C., Xu, K., Wang, F. and Wang, H. (2013), “Predicting information diffusion initiated from multiple sources in online social networks”, 2013 Sixth International Symposium on Computational Intelligence and Design, Vol. 2, pp. 96-99. Pinto, H., Almeida, J.M. and Gonçalves, M.A. (2013), “Using early view patterns to predict the popularity of youtube videos”, Proceedings of the Sixth ACM International Conference on Web Search and Data Mining, se WSDM ’13, ACM, New York, NY, pp. 365-374, doi: 10.1145/ 2433396.2433443. Rodriguez, M., Leskovec, J. and Scholkopf, B. (2013), “Modeling information propagation with survival theory”, Proc. Int. Conf. Mach. Learn, pp. 666-674. Rodriguez, M.G., Leskovec, J., Balduzzi, D. and Schölkopf, B. (2014), “Uncovering the structure and temporal dynamics of information propagation”, Network Science, Vol. 2 No. 1, pp. 26-65. Shahsavari, M. and Golpayegani, A.H. (2017), “Finding k-most inﬂuential users in social networks for Evolutionary information diffusion based on network structure and different user behavioral patterns”, 2017 information IEEE 14th International Conference on e-Business Engineering (ICEBE), Nov 2017, pp. 220-225. dynamics Tsai, C., Lou, J., Lu, W. and Lin, S. (2014), “Exploiting rank-learning models to predict the diffusion of preferences on social networks”, 2014 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2014), pp. 265-272. Usui, S., Toriumi, F., Hirayama, T. and Mase, K. (2013), “Analysis of inﬂuential features for information diffusion”, 2013 International Conference on Social Computing, pp. 905-908. Wang, B., Chen, G., Fu, L., Song, L. and Wang, X. (2017), “Drimux: dynamic rumor inﬂuence minimization with user experience in social networks”, IEEE Transactions on Knowledge and Data Engineering, Vol. 29 No. 10, pp. 2168-2181. Weibull, J.W. (1997), Evolutionary Game Theory, Vol. 265, The MIT Press, Cambridge, MA. Weng, L., Menczer, F. and Ahn, Y.-Y. (2014), “Predicting successful memes using network and community structure”, Proc. 8th AAAI Int. Conf. Weblogs Soc. Media, pp. 535-544. Yagan, O., Qian, D., Zhang, J. and Cochran, D. (2013), “Conjoining speeds up information diffusion in overlaying social-physical networks”, IEEE Journal on Selected Areas in Communications, Vol. 31 No. 6, pp. 1038-1048. Yang, J. and Leskovec, J. (2010), “Modeling information diffusion in implicit networks”, 2010 IEEE International Conference on Data Mining, pp. 599-608. Yu, W., Gao, C., Guojie, S. and Kunqing, X. (2010), “Community-based greedy algorithm for mining top- kinﬂuential nodes in mobile social networks”, Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ser. KDD ’10, ACM, New York, NY, pp. 1039-1048, doi: 10.1145/1835804.1835935. Yuan, C. and Ji, D. (2019), “Stochastic asymptotically stability of an information diffusion model with random perturbation in social network”, 2019 IEEE 8th Joint International Information Technology and Artiﬁcial Intelligence Conference (ITAIC), pp. 1916-1920. Further reading Wikipedia “Evolutionary game theory”, available at: https://en.wikipedia.org/wiki/Evolutionary_game_theory Wikipedia “Social network”, available at: http://en.wikipedia.org/wiki/Social_network Corresponding author Hangjing Zhang can be contacted at: zhanghangjing@std.uestc.edu.cn For instructions on how to order reprints of this article, please visit our website: www.emeraldgrouppublishing.com/licensing/reprints.htm Or contact us for further details: permissions@emeraldinsight.com http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Crowd Science Emerald Publishing http://www.deepdyve.com/lp/emerald-publishing/evolutionary-information-dynamics-over-social-networks-a-review-XDi8709dWl

Loading next page...

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher: Emerald Publishing
Copyright: © Hangjing Zhang, Yan Chen and H. Vicky Zhao.
ISSN: 2398-7294
DOI: 10.1108/ijcs-09-2019-0026
Publisher site: See Article on Publisher Site

Abstract

Purpose – The purpose of this paper is to have a review on the analysis of information diffusion based on evolutionary game theory. People now get used to interact over social networks, and one of the most important functions of social networks is information sharing. Understanding the mechanisms of the information diffusion over social networks is critical to various applications including online advertisement and rumor control. Design/methodology/approach – It has been shown that the graphical evolutionary game theory (EGT) is a very efﬁcient method to study this problem. Findings – By applying EGT to information diffusion, the authors could predict every small change in the process, get the detailed dynamics and ﬁnally foretell the stable states. Originality/value – In this paper, the authors provide a general review on the evolutionary game-theoretic framework for information diffusion over social network by summarizing the results and conclusions of works using graphical EGT. Keywords Crowd behaviour analysis, Information diffusion, Evolutionary game theory Paper type Literature review 1. Introduction Nowadays, people cannot live in individual. They have to depend on their social networks more or less and interact with others. A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. Typical social network examples include Facebook/Twitter networks, hyperlink networks of websites, scientiﬁc collaboration/citation networks and Internet of Things (IoT) (Wikipedia). With the rapid development of the internet and mobile technologies, social networks are of extremely large scale, e.g. there are over 2.41 billion monthly active users and 1.59 billion daily active users worldwide on Facebook as of June © Hangjing Zhang, Yan Chen and H. Vicky Zhao. Published in International Journal of Crowd Science. Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original International Journal of Crowd publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/ Science by/4.0/legalcode pp. 45-59 Emerald Publishing Limited This work is supported by the National Key Research and Development Program of China 2398-7294 (2017YFB1400100). DOI 10.1108/IJCS-09-2019-0026 2019 (Noyes, 2019). Meanwhile, the information size on the social networks is becoming even IJCS tremendous-scale. For instance, averagely 277,777 stories are posted on Instagram, 4,500,000 4,1 videos are watched on YouTube, 511,200 tweets are sent on Twitter and 510,000 comments are posted on Facebook in every minute (Noyes, 2019; DOMO, 2019; Martin, 2019). The information disseminated over social networks is of various kinds, e.g. when a total victory happens in a sport match, some political opinions are declared by a party or politics, some deal advertisements are released, titbits or rumors about a superstar are exposed to the public. All these information would experience the process of generation, dissemination and vanishment, and the most important part is the information diffusion. One piece of information may disappear quickly after the appearing, or last for a long time and inspire a heated discussion for its value. To ﬁgure out how the information spreads over social networks, simulating the process of information diffusion or even predicting the ﬁnal destiny of a piece of new information is vital in many applications. From users’ perspective, the diffusion dynamics or the popularity of the information is determined by complicated interactions and decision-making of other users. Based on different people’s preferences, the surrounding neighbors’ actions, the reliability of the information and many other factors, users would choose to spread information accordingly. For example, when a consumer comes across an advertisement of a new product, he or she would decide whether to trust or further diffuse it according to the comments of friends, the reputation of information publisher and manufacturer, and possibly his or her initial impression. Of course if the consumer is a fan of the product, he or she tends to share this message over social networks, which tightens the connection between the consumer and the information sender. However, if the consumer isn’t interested in it at all, he or she may regard the information spreader as worthless, and thus choose to cut the connection. In practice, the mechanisms in the process of information diffusion should be explored in depth. The study of information diffusion originates from the research of computer virus/ epidemic spreading over networks (Pastor-Satorras and Vespignani, 2001). One of the earliest and prominent works about information diffusion is (Gruhl et al.,2004), which studied the dynamics of information propagation through blogspace from both macroscopic and microscopic points of views. Subsequently, there are numerous works on the information diffusion, and researchers explore the problem from different aspects and adopt multiple methods to solve it. From the view of study object, the existing works can be divided into three categories: (1) diffusion characteristics analysis; (2) diffusion dynamics analysis; and (3) diffusion stability analysis. Among the ﬁrst category, Masahiro et al. (2009) discussed how to extract the most inﬂuential nodes on a large-scale social network in (Kimura et al., 2007). Later, many methods were proposed to mine top-k inﬂuential nodes in mobile social networks, e.g. a community-based greedy algorithm in Yu et al. (2010), the Shapley value-based Inﬂuential Nodes algorithm in Narayanam and Narahari (2011) and content-based improved greedy algorithm in Shahsavari and Golpayegani (2017) which decreased the total amount of computations. Authors in Usui et al. (2013) proposed a network growth model that can produce networks that have the necessary features for analysis and also analyzed how each feature affects information diffusion. The second category focuses on analyzing the dynamic diffusion process over different kinds of networks using different mathematical models (Damon, 2010; Yagan et al.,2013). In Damon (2010), the authors studied how a social Evolutionary network affected the spread of behavior and investigated the effects of network structure on information users’ behavior diffusion. Rather than focusing on the behavior diffusion, Bakshy et al. dynamics (2012). Studied the role of social networks in general information diffusion through an experimental approach. As online social networks, e.g. Facebook and Twitter, became more and more popular, some empirical analysis were conducted using large-scale datasets, including predicting the speed and range of information diffusion on Twitter (Jiang and Scott, 2010), modeling the global inﬂuence of a node on the rate of diffusion on Memetracker (Yang and Leskovec, 2010) and illustrating the statistical mechanics of rumor spreading on Facebook (Ostilli et al.,2010). Moreover, the information diffusion on overlaying social- physical networks was analyzed in Yagan et al. (2013). The third category of information diffusion analysis focuses on the stability and consequence of information diffusion (Peng et al., 2013; Kuhnle et al., 2018). In Peng et al. (2013), the conditions for information diffusion vanishing and information diffusion being persistent in social networks were studied. Peng et al. used a mathematical model to predict the information diffusion process of multi-source news and validated its accuracy (Yuan and Ji, 2019). How to restrain the private or contaminated information diffusion was studied in Masahiro et al. (2009) and Ilyas et al. (2011) through identifying the important information links and hubs, respectively. How to maximize information diffusion through a network was discussed in Kim and Yoneki (2012) by designing effective neighbors selection strategies, whereas in Kuhnle et al. (2018), authors proposed approximation algorithms to realize the inﬂuence maximization. From the view of adopted method, works could also be classiﬁed into two categories. The ﬁrst category focuses on macro exploration, usually adopting machine learning or data mining techniques to predict the dynamics or properties of network. Among the ﬁrst category, Pinto et al. used early diffusion data to predict future diffusion (Pinto et al.,2013) while the community structure was further exploited to improve the performance of prediction of viral memes in Weng et al. (2014). Given the information diffusion data, efﬁcient algorithms were developed to infer the underlying information diffusion network in Rodriguez et al. (2014), Rodriguez et al. (2013) and Gomez Rodriguez et al. (2013). Hao et al. (2014). proposed a matrix factorization based predictive model and used gradient descent to optimize objective function (Hao et al.,2014), whereas in Alsuwaidan and Ykhlef (2017),a novel model based on a physical radiation energy transfer mechanism was proposed to predict the diffusion graph of a certain contagion. Authors in Tsai et al. (2014) studied diffusion of preference on social networks by a rank-learning based data-driven approach. Jiang et al. (2015) proposed a K-center method to realize multi-source identiﬁcation of information diffusion and the corresponding infection regions in general networks. In Chejara and WilfredGodfrey (2018), authors presented an analysis of various heuristic based inﬂuence maximization techniques and proposed a machine learning based approach to ﬁnd the spread of information in the network. A common limitation of these ML or data mining based approaches is the lack of understanding of the underlying microscopic mechanisms of the individuals’ decision-making that dominate the information diffusion process, which is the focus of the papers in the second category. The second category models the information diffusion from the microscopic aspect, emphasizing more on the decisions and motivations of individuals. Assuming each user played the best response to the population’s strategies, Morris studied the conditions for global contagion of behaviors (Morris, 2000). The authors in Lin et al. (2013) studied the problem of predicting dynamic trends according to each users’ activeness under a dynamic activeness model. Based on the correlation, Lee and Chung (2014) proposed a probabilistic model to estimate the probability of a user’s adoption of the naive Bayes classiﬁer. A game-theoretic framework for the study of competition between ﬁrms IJCS who aimed to maximize adoption of their products by consumers located in a social network 4,1 was proposed in Goyal and Kearns (2012) and Fazeli and Jadbabaie (2012). Ding et al. (2017), Jin-lou et al. (2011) and Wang et al. (2017) proposed information diffusion models to study the spreading by deﬁning different objective functions for each user and then solving the corresponding minimization or maximization problem. To fully understand the details in information diffusion and simulate the whole process including diffusion dynamics as well as the consequence of information, in recent years some researchers put forward a novel model based on graphical evolutionary game theory (EGT). Authors in Jiang et al. (2014) and Jiang et al. (2014) proposed an evolutionary game- theoretic framework to model the dynamic information diffusion process among nodes in social networks, where the authors in Jiang et al. (2014) paid more attention to the ﬁnal stable state, while in Jiang et al. (2014), the emphasis was on the evolutionary dynamics in Cao et al. (2016) then extended the analysis of the information diffusion process to the heterogeneous social networks where nodes can have different types. In these works, the model was proved to be rather effective in accuracy, with less calculation compared with ML or data mining approaches. Based on the conclusions in the evolutionary game-theoretic framework, the dynamics and stable states in the process of information diffusion could be quickly predicted, and as a result to be applied to plenty areas such as online advertisements, rumor control and network security. Therefore, in this paper, we have a review on these works that focus on information diffusion analysis based on evolutionary game-theoretic model. We summarize the system framework and key conclusions to illustrate how the graphical EGT can be used to model information diffusion. The rest of the paper is organized as follows. Section 2 introduces evolutionary game theory, describes the graphical EGT in detail and gives some basic concepts of them. The evolutionary game-theoretic system framework and analysis results of several cases are shown in Section 3 Conclusions are drawn in Section 4. 2. Graphical evolutionary game theory and the correspondence of information diﬀusion Initially, EGT is a biological concept, starting with the problem of how to explain ritualized animal behaviour in a conﬂict situation (Wikipedia), and developing to make up for traditional game theory’s defects. In classical game theory, players are required to make rational choices, which means they should carefully consider sophisticated reasonings like what they want, what their opponents want and what their opponents know and determine the optimal strategies in competitions. Evolutionary game theory, on the other hand, does not require players to act rationally and assumes very little about the reasoning processes of the players. It focuses on the process of natural selection, i.e. evolution. It deﬁnes a framework of contests, strategies and the mathematical criteria that can be used to predict the performances of competing strategies. The results of a game include the dynamics of changes in the population, the success of strategies and any equilibrium states reached. These basic elements in a game could just correspond with the things in the process of information diffusion. We could regard the whole information diffusion process as a game, for users being players, their adopted strategies being the strategies in the game, the process of information spreading being the evolution and the consequence of information (survive or vanish, and if survive, how many users accept this piece of information) being the equilibrium states. Different from methods using a large amount of data, by applying EGT to information diffusion, we could predict every small change in the process, get the detailed dynamics and ﬁnally foretell the stable states. We are able to interpret the mechanisms of how users interact with others from the view of individuals themselves instead of the whole Evolutionary network, which helps us understand the diffusion more deeply. information Due to the structure of social network with intricate connections between users, dynamics graphical presentation of the network is combined with EGT to analyze the information dissemination as it makes problem more visualized. The social network graph is shown in Figure 1. As it shows, nodes with different colors represent different kinds of users in heterogeneous social network, and edges represent the connections between users. If users are treated as homogeneous individuals, nodes with different colors are identical in the analysis. In the model, users only have two strategies: forwarding the information and not forwarding. For the center user with a certain amount of neighbors, the numbers of his neighbor nodes adopting forwarding strategy and not forwarding strategy are certainly available. For two users with the connection, by interacting with each other with their own strategies, both sides would get same instant payoff, which equals to the beneﬁtof interaction and could be obtained according to a predeﬁned payoff matrix. Based on the payoff, we could calculate the ﬁtness of every user, involving baseline ﬁtness, payoffs and selection intensity. Baseline ﬁtness represents the player’s inherent property, e.g. a user’s own interests on the released news in a social network. In this framework, the baseline ﬁtness is normalized as one. Payoffs are determined by the payoff matrix and the graph structure. As for selection intensity, it is the relative contribution of the game to ﬁtness. When selection intensity approaches zero, it indicates the limit of weak selection (Ohtsuki et al.,2007), while selection intensity approaching one denotes strong selection, where ﬁtness equals payoffs. Here the weak selection is assumed thus selection intensity is a quite small value. After introducing ﬁtness, how to update the strategy should be deﬁned. There are many strategy updating rules from the evolutionary biology ﬁeld and they are used to model the resident/mutant evolution process. According to Ohtsukia and Nowak (2006), there are three typical and prevalent strategy updating rules: birth-death (BD), death-birth (DB) and imitation (IM) (shown in Figure 2). (1) BD updating rule: a player is chosen for reproduction with the probability being proportional to ﬁtness (Birth process). Then, the chosen player’s strategy replaces one neighbor’s strategy with uniform probability (Death process). (2) DB updating rule: a random player is chosen to abandon his/her current strategy (Death process). Then, the chosen player adopts one of his/her neighbors’ strategies with the probability being proportional to their ﬁtness (Birth process). Figure 1. An illustration of the social network IJCS 4,1 Figure 2. Three different update rules, where death selections are shown in dark blue and birth selections are shown in red (3) IM updating rule: each player either adopts the strategy of one neighbor or remains his/her current strategy, with the probability being proportional to ﬁtness. From Jiang et al. (2014), we know that the analyses of these three updating rules are similar, and the results are equivalent under weak selection scenario when the network degree is sufﬁciently large. Once a new piece of information is released by a user, other users are expected to receive the information and retransmit it to more. However, whether to forward the information depends on different users’ own choices, i.e. their strategies. Therefore, by analyzing the dynamics of users’ strategies on information forwarding, we can infer how the information propagates to other users, how popular the information is, and then ﬁnally what’sthe result of the information. To get the dynamics, ﬁrstly, the global and local network states should be deﬁned: global population state p , representing the proportion of population using the strategy; global edge state p , representing the proportion of edges with speciﬁc strategies; ij and local network state p , representing the proportion of a user’s neighbors adopting ijj the strategy. Among these notations i and j indicate different strategies, and in the model they can only be Evolutionary f for forwarding and n for not. To analyze the dynamic changing along with time, we information discretize the information diffusion process into time slots. In each time slot, users are able to dynamics observe the strategies of other adjacent users in the population. Based on the observed information, in the next time slot, each user decides on whether forwarding the information by ﬁnding out which strategy can give higher ﬁtness. Thus, as the users’ strategies update slot by slot, the network state also keeps changing slot by slot. Therefore, the evolutionary dynamics are deﬁned as the variation between every two time slots. To simplify the problem, network state and dynamics that only related to the forwarding strategy are considered, so corresponding dynamics of states are as follows: population dynamics p : dynamics of global population state, illustrating the dynamics of whole network; relationship dynamics p : dynamics of global edge state, illustrating the dynamics ff of relationship among users; and inﬂuence dynamics p : dynamics of local network state, illustrating the inﬂuence of f jf one user on his/her neighbors. As the information spreading process proceeds, the whole network would gradually reach an evolutionary stable state (ESS), i.e. all players tend to adopt their optimal stable strategies (Weibull, 1997). Intuitively, when the whole population is adopting optimal strategy, a small group of invaders using any alternate strategies should have strictly lower ﬁtness than the users of the majority, and eventually die off with a high probability. The ﬁnal ESSs can be found at the stable points of different kinds of dynamics. In summary, graph structure, players, strategy, ﬁtness (payoff) and ESS are ﬁve basic elements of a graphical evolutionary game, and these elements have perfect corresponding contents in information diffusion analysis as stated above (brieﬂy shown in the Table I), which proves that EGT is a practical and effective method to analyze information diffusion. 3. Analysis framework and results of several cases Based on the deﬁnition in graphical EGT and the coherence of information diffusion over social network, the information propagation could be studied through characteristics stated before, especially the evolutionary dynamics and ESSs which are the two most important things in the evolutionary game-theoretic framework. No matter which strategy updating rule is adopted, ESS is concluded based on the analysis of evolutionary dynamics. The basic framework of analysis can be summarized as follows. Above all, to calculate each user’s ﬁtness, we need a certain amount of neighbors adopting forwarding strategy and not forwarding strategy. However, this number is not known in every time slot during Graphical EGT Social network Table I. Graph structure Social network topology Correspondence Players Users in the social network between graphical Strategy forward the information or not EGT and social Fitness Utility from forwarding or not ESS Stable information diffusion state network prediction of detailed changing process, so we have to get its distribution. On account of the IJCS assumption that the social network is large enough, it’s reasonable to treat global population 4,1 state p or local network state p as the probability of center user encountering neighbors i ijj adopting strategy i. Thus, when the total number of neighbor nodes is given, the distribution of the number of neighbor nodes adopting every strategy is available. Based on this number, predeﬁned baseline ﬁtness, payoffs and selection intensity, each user’s ﬁtness could be obtained. Then according to the strategy updating rule, the probability of a user being chosen to reproduction or updating his/her strategy is proportional to the ﬁtness in a manner. With the probability of users’ strategy changing, we can know the probability for the increase or decrease of evolutionary states, which is exactly the evolutionary dynamics that we look for. One common method to ﬁnd ESS is to set the differential of state as zero, i.e. set the evolutionary dynamics as zero. Settle the equation and then the ESS under different conditions could ﬁnally be shown. Using the derived formula of evolutionary dynamics and ﬁnal ESS, we are able to predict the evolutionary process in every time slot, and foretell the stable states of the information diffusion, e.g. how many users still forwarding this piece of message in the social network. Here we seek out several different network structures to illustrate the framework. 3.1 Analysis of homogeneous network 3.1.1 Results over uniform degree network. In the uniform scenario, the social network based on a homogenous graph with the same degree for all users is considered. In other words, in this kind of social network, there is no difference between all users and they could be regarded as a whole of one type. Meanwhile, every user has the same number of neighbor nodes. The main reason to discuss the uniform degree network is to provide more insight into the complicated problem of information diffusion, and the derivation and results (e.g. the ﬁtness calculation and dynamics derivations) of the uniform degree network analysis will be used in the non-uniform degree case. Under the weak selection, the dynamics and ESSs could be derived in a close form. According to the formula of population dynamics, it only relies on the initial population state, the values of payoff matrix and the degree of the network, regardless of the network scale information. Therefore, the population dynamics of information diffusion over uniform degree networks show the scale-free property. Moreover, the formulashows that thedynamicisanincreasingfunctioninterms of thepayoffthat both sides adopt forwarding strategy. The corresponding physical meaning is that when the higher payoff can be obtained by forwarding the information, the increasing rate will also be higher. On the other hand, if not forwarding the information can gain higher payoff, the increasing rate will be lower, which is just the reason why population dynamic is a decreasing function in terms of the payoff that both users do not forward the information. For the formula of relationship dynamics and inﬂuence dynamics, they are functions involving themselves and also the population dynamics, which are more sophisticated. Based on the evolutionary dynamics analysis, the evolutionary stable network state could be obtained by solving equations. There are three scenarios of ESSs, which are respectively one under the case of u > u > u , zero when u > u > u , and a value ff fn nn nn fn ff between zero and one under other conditions, where u represents the payoff that both sides ff forward information and u , u are deﬁned in the same way. Zero and one are two extreme fn nn stable states, representing that no user forward the information and all users forward the information, respectively. When the population state is one, it means that both users forwarding the information can gain the most payoff, while not forwarding gains the least payoff. In a social network, this is corresponding to the scenario where the released Evolutionary information is an extremely hot topic, forwarding which can attract more attentions. On the information contrary, things are just the opposite when population stable state is zero, which is dynamics corresponding to the scenario where the released information is useless or negative advertisement, forwarding which can only incur unnecessary cost. As for the third ESS that between zero and one, there are two other cases, one of which is u > u , u > u . In this fn nn fn ff case, unilateral forwarding can bring more payoff than no forwarding or both forwarding. In a social network, this case is corresponding to the scenario where both users forwarding the information can gain only limited reward but incur more cost to both of them. An example of this case can be that the information is not the mainstream topic, e.g. the news about a punk musician and is supposed to be diffused among people with similar interests. In the other case that u > u , u > u , the payoff conﬁguration is equivalent to that of the nn fn ff fn coordination game, where both players with the same actions can make more payoff than opposite actions. An example of this case can be that the information is politically sensitive and its reality is not guaranteed, forwarding which may gain attractions but also incur potential misleading cost. In Figure 3, conclusions are veriﬁed in a synthetic network which is a homogeneous uniform degree network in four different scenarios: (1) Case 1: u = 0.8 > u = 0.6 > u = 0.4; ff fn nn (2) Case 2: u = 0.8 > u = 0.6 > u = 0.4; fn ff nn (3) Case 3: u = 0.8 > u = 0.6 > u = 0.4; and fn nn ff (4) Case 4: u = 0.8 > u = 0.6 > u = 0.4. nn fn ff From Figure 3, we can see that all the simulation results are consistent with the theoretical results, which prove the correctness of the conclusions. 3.1.2 Results over non-uniform degree network. In the non-uniform scenario, social network is based on a graph whose degree exhibits a speciﬁc distribution. This distribution means that when randomly choosing one user on the network, the probability of the chosen user with speciﬁc neighbors is a speciﬁc distribution. Note that degree correlation is not taken into account, i.e. the degrees of all users are independent of each other. So when some Figure 3. Simulation results for synthetic network which is the homogeneous uniform degree network new information is released, all users update their information forwarding strategies in a IJCS spontaneous manner. The procedure and conclusions of analysis are similar to those in 4,1 uniform degree network, and the biggest difference is that probability distribution of degree is introduced so the expectation and variance appear in the formula. Results are shown in the Figure 4, in which Erd†os-Rényi random network is adopted as non-uniform degree network in the simulation. Four cases are the same as before, and the simulation results agree well with the theoretical results. In Figure 5, the comparison of proposed model and one of the existing data mining method in Leskovec et al. (2009) is exhibited. Payoff matrices are determined by estimating using the Twitter hashtag data set. The vertical axis is the dynamics, and the mention times of different hashtags per hour in the Twitter dataset are normalized within interval and denoted by solid black square. From the ﬁgure, we can see that the graphical EGT model can ﬁt the real-world information diffusion dynamics better than the data mining method in Leskovec et al. (2009), as users’ interactions and decision-making behaviors are taken into account. 3.2 Analysis of heterogeneous network 3.2.1 Results for unknown user type model. In social network, as people have different habits and interests, there may be lots of types of users, which could be modeled as a heterogeneous network. For example, if a group of people are all sports fans, they belong to the same type considering forwarding information related to sports, while some other people belong to music lovers. Therefore, the payoff matrices of a piece of information for different types are different. When users get in touch with each other at ﬁrst, they are not familiar with each other, so they may not know which type his/her neighbors belong to, corresponding to the unknown user type model. Analyzing every type of users respectively, the dynamics of population state of each type could be deduced separately. By proportional combination, we are able to get the global evolutionary dynamics. It can be observed that the dynamic of each type not only consists of itself but also the dynamics of global state, which means that nodes are affected not only by those with the same type, but also all other nodes. Similarly, by setting the dynamics as zero, Figure 4. Simulation results for Erd†os-Rényi random network which is a homogeneous non- uniform degree network Evolutionary information dynamics (a) (b) Figure 5. (c) (d) Comparison with the existing work Notes: (a) Googlewave; (b) DavidArchuleta; (c) NIN; (d) Tehran three ESSs with different payoff matrices are derived in a close form. Figure 6 shows the simulation results of unknown user type model when the payoff matrices are set ðÞ ðÞ ðÞ ðÞ ðÞ ðÞ as: u 1 ¼ 0:4; u 1 ¼ 0:6; u 1 ¼ 0:3; u 2 ¼ 0:2; u 2 ¼ 0:4; u 2 ¼ 0:5. The nn nn ff fn ff fn theoretical dynamics ﬁt the simulation dynamics well and ESSs are predicted accurately. The average relative ESS error of the heterogeneous model is 3.54 per cent. 3.2.2 Results for known user type model. Sometimes, through repeated interactions, users may somehow manage to know their neighbors’ types. For instance, when a user observes that one of his friends frequently posts news about football match, he may gradually know that this friend is a football fan. This condition could be modeled as known user type. In other words, when the center user is deciding on whether to change the strategy, he/she treats his/her neighbors in different ways for knowing their types. As a user’s type and strategy affect its neighbors’ payoffs, they may also inﬂuence the neighbors’ strategies. Thus the edge information, i.e. relationship state (global edge state) and inﬂuence state (local network state) are required to fully characterize the network state. In the ﬁnal formulation of dynamics, it could be proved that the relationship dynamics and inﬂuence dynamics change at a much faster speed than population dynamics do. This implies that we can select a time window with an appropriate length such that the population dynamics basically remain unchanged while the relationship dynamics and inﬂuence dynamics vary a lot. So we focus on a small time period where the population dynamics do not vary with time while the inﬂuence dynamics vary. Next, it is shown that in this small time period, the inﬂuence 䣉䣣䣯䣧䢢䣶䣪䣧䣱䣴䣧䣶䣫䣥䣉䣣䣯䣧䢢䣶䣪䣧䣱䣴䣧䣶䣫䣥䣉䣣䣯䣧䢢䣶䣪䣧䣱䣴䣧䣶䣫䣥䣉䣣䣯䣧䢢䣶䣪䣧䣱䣴䣧䣶䣫䣥 IJCS 4,1 Figure 6. Simulation results of the evolutionary dynamics for the unknown user type model dynamics will converge to the corresponding population dynamics. Simulation results in Figure 7 demonstrate that the known user type model based theoretical dynamics and the simulated dynamics match well. In Figure 7, the evolutionary dynamics given by the theory of the unknown user type model are also plotted. This does not match the simulated evolutionary dynamics under the known user type model, indicating the necessity for the theory of the known user type model. 4. Conclusions In this paper, we summarize the results from works that analyze information diffusion process based on graphical evolutionary game theory over social network. To ﬁgure out the features in the process, evolutionary dynamics and evolutionary stable state are discussed. And it is found that the analysis of information diffusion based on graphical EGT matches well with reality. In the future, social network with irrational users or malicious users should also be considered, which would be more complicated compared with networks only consist of rational users. How to model the behaviours of irrational users is the focus of future research. Figure 7. Simulation of evolutionary dynamics: the known user type model References Evolutionary Alsuwaidan, L. and Ykhlef, M. (2017), “Information diffusion predictive model using radiation information transfer”, IEEE Access, Vol. 5, pp. 25946-25957. dynamics Bakshy, E., Rosenn, I., Marlow, C. and Adamic, L. (2012), “The role of social networks in information diffusion”, Proc.21stInt. Conf. World Wide Web (WWW), pp. 519-528. Cao, X., Chen, Y., Jiang, C. and Ray Liu, K.J. (2016), “Evolutionary information diffusion over heterogeneous social networks”, IEEE Transactions on Signal and Information Processing over Networks, Vol. 2 No. 4, pp. 595-610. Chejara, P. and WilfredGodfrey, W. (2018), “Machine learning based method to predict inﬂuence spread”, 2018 8th International Conference on Cloud Computing, Data Science Engineering (Conﬂuence), pp. 268-273. Damon, C. (2010), “The spread of behavior in an online social network experiment”, Science, Vol. 329 No. 5996, pp. 1194-1197, available at: https://science.sciencemag.org/content/329/5996/1194 Ding, X., Wu, Z., Chen, W., Liu, Y., Xie, Y. and Cai, S. (2017), “Modeling complex social contagions in big data era”, 2017 IEEE 2nd Advanced Information Technology, Electronic and Automation Control Conference (IAEAC), pp. 830-834. DOMO (2019), “Data never sleeps 7.0”, available at: www.domo.com/learn/data-never-sleeps-7 Fazeli, A. and Jadbabaie, A. (2012), “Game theoretic analysis of a strategic model of competitive contagion and product adoption in social networks”, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), pp. 74-79. Gomez Rodriguez, M., Leskovec, J. and Schölkopf, B. (2013), “Structure and dynamics of information pathways in online media”, Proceedings of the Sixth ACM International Conference on Web Search and Data Mining, se WSDM ’13. ACM, New York, NY, pp. 23-32, doi: 10.1145/ 2433396.2433402. Goyal, S. and Kearns, M. (2012), “Competitive contagion in networks”, Proceedings of the Forty-fourth Annual ACM Symposium on Theory of Computing, se STOC ’12. ACM, New York, NY, pp. 759-774, doi: 10.1145/2213977.2214046. Gruhl, D., Guha, R., Liben-Nowell, D. and Tomkins, A. (2004), “Information diffusion through blogspace”, Proc. 13rd Int. Conf. World Wide Web (WWW), pp. 491-501. Hao, X., Sheng, G., Yu, Z., Juncen, L., Huacan, P. and Jun, G. (2014), “Predicting information diffusion via matrix factorization based model”, 2014 4th IEEE International Conference on Network Infrastructure and Digital Content, pp. 257-261. Ilyas, M.U., Shaﬁq, M.Z., Liu, A.X. and Radha, H. (2011), “A distributed and privacy preserving algorithm for identifying information hubs in social networks”, 2011 Proceedings IEEE INFOCOM, pp. 561-565. Jiang, Y. and Scott, C. (2010), “Predicting the speed, scale, and range of information diffusion in twitter”, Conference: Proceedings of the Fourth International Conference on Weblogs and Social Media, available at: www.microsoft.com/en-us/research/publication/predicting-speed-scale-range- information-diffusion-twitter/ Jiang, C., Chen, Y. and Liu, K.J.R. (2014), “Graphical evolutionary game for information diffusion over social networks”, IEEE Journal of Selected Topics in Signal Processing, Vol. 8 No. 4, pp. 524-536. Jiang, C, Chen, Y. and Liu, K.J.R. (2014), “Evolutionary dynamics of information diffusion over social networks”, IEEE Transactions on Signal Processing, Vol. 62 No. 17, pp. 4573-4586. Jiang, J., Wen, S., Yu, S., Xiang, Y. and Zhou, W. (2015), “K-center: an approach on the multi-source identiﬁcation of information diffusion”, IEEE Transactions on Information Forensics and Security, Vol. 10 No. 12, pp. 2616-2626. Jin-Lou, Z., Zhi-bin, L. and Jian-Nan, Y. (2011), “Modeling of information diffusion based on network dimension-force”, 2011 International Conference on Management Science Engineering 18th Annual Conference Proceedings, pp. 18-27. Kim, H. and Yoneki, E. (2012), “Inﬂuential neighbours selection for information diffusion in online IJCS social networks”, 2012 21st International Conference on Computer Communications and 4,1 Networks (ICCCN), pp. 1-7. Kimura, M., Saito, K. and Nakano, R. (2007), “Extracting inﬂuential nodes for information diffusion on a social network”, Prof. of AAAI Conf. Artif. Intell, pp. 1371-1376. Kuhnle, A., Alim, M.A., Li, X., Zhang, H. and Thai, M.T. (2018), “Multiplex inﬂuence maximization in online social networks with heterogeneous diffusion models”, IEEE Transactions on Computational Social Systems, Vol. 5 No. 2, pp. 418-429. Lee, J.-R. and Chung, -W. (2014), “A new correlation-based information diffusion prediction”, Proceedings of the 23rd International Conference on World Wide Web, ser. WWW ’14 Companion, ACM, New York, NY, pp. 793-798, doi: 10.1145/2567948.2579241. Leskovec, J., Backstrom, L. and Kleinberg, J. (2009), “Meme-tracking and the dynamics of the news cycle”, Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, se KDD ’09, ACM, New York, NY, pp. 497-506, doi: 10.1145/1557019.1557077. Lin, S., Kong, X. and Yu, P.S. (2013), “Predicting trends in social networks via dynamic activeness model”, Proceedings of the 22nd ACM International Conference on Conference on Information & Knowledge Management, se CIKM ’13, ACM, New York, NY, pp. 1661-1666, doi: 10.1145/ 2505515.2505607. Martin, N. (2019), “How much data is collected every minute of the day”, available at: www.forbes.com/ sites/nicolemartin1/2019/08/07/how-much-data-is-collected-every-minute-of-the-day Masahiro, K., Kazumi, S. and Hiroshi, M. (2009), “Blocking links to minimize contamination spread in a social network”, ACM Trans. Knowl. Discov. Data, Vol. 3 No. 2, pp. 9:1-9:23, doi: 10.1145/ 1514888.1514892. Morris, S. (2000), “Contagion”, Review of Economic Studies, Vol. 67 No. 1, pp. 57-78. Narayanam, R. and Narahari, Y. (2011), “A shapley value-based approach to discover inﬂuential nodes in social networks”, IEEE Transactions on Automation Science and Engineering, Vol. 8 No. 1, pp. 130-147. Noyes, D. (2019), “The top 20 valuable facebook statistics c updated september 2019”, available at: https://zephoria.com/top-15-valuable-facebook-statistics/ Ohtsukia, H. and Nowak, M.A. (2006), “The replicator equation on graphs”, Journal of Theoretical Biology, Vol. 243 No. 1, pp. 86-97. Ohtsuki, H., Nowak, M.A. and Pacheco, J.M. (2007), “Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs”, Physical Review Letters, Vol. 98 No. 10, p. 108106. Ostilli, M., Yoneki, E., Leung, I.X., Mendes, J.F., Lio, P. and Crowcroft, J. (2010), “Statistical mechanics of rumor spreading in network communities”, Proc. Int. Conf. Comput. Sci., pp. 2331-2339. Pastor-Satorras, R. and Vespignani, A. (2001), “Epidemic spreading in scale-free networks”, Physical Review Letters, Vol. 86 No. 14, pp. 3200-3203. Peng, C., Xu, K., Wang, F. and Wang, H. (2013), “Predicting information diffusion initiated from multiple sources in online social networks”, 2013 Sixth International Symposium on Computational Intelligence and Design, Vol. 2, pp. 96-99. Pinto, H., Almeida, J.M. and Gonçalves, M.A. (2013), “Using early view patterns to predict the popularity of youtube videos”, Proceedings of the Sixth ACM International Conference on Web Search and Data Mining, se WSDM ’13, ACM, New York, NY, pp. 365-374, doi: 10.1145/ 2433396.2433443. Rodriguez, M., Leskovec, J. and Scholkopf, B. (2013), “Modeling information propagation with survival theory”, Proc. Int. Conf. Mach. Learn, pp. 666-674. Rodriguez, M.G., Leskovec, J., Balduzzi, D. and Schölkopf, B. (2014), “Uncovering the structure and temporal dynamics of information propagation”, Network Science, Vol. 2 No. 1, pp. 26-65. Shahsavari, M. and Golpayegani, A.H. (2017), “Finding k-most inﬂuential users in social networks for Evolutionary information diffusion based on network structure and different user behavioral patterns”, 2017 information IEEE 14th International Conference on e-Business Engineering (ICEBE), Nov 2017, pp. 220-225. dynamics Tsai, C., Lou, J., Lu, W. and Lin, S. (2014), “Exploiting rank-learning models to predict the diffusion of preferences on social networks”, 2014 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2014), pp. 265-272. Usui, S., Toriumi, F., Hirayama, T. and Mase, K. (2013), “Analysis of inﬂuential features for information diffusion”, 2013 International Conference on Social Computing, pp. 905-908. Wang, B., Chen, G., Fu, L., Song, L. and Wang, X. (2017), “Drimux: dynamic rumor inﬂuence minimization with user experience in social networks”, IEEE Transactions on Knowledge and Data Engineering, Vol. 29 No. 10, pp. 2168-2181. Weibull, J.W. (1997), Evolutionary Game Theory, Vol. 265, The MIT Press, Cambridge, MA. Weng, L., Menczer, F. and Ahn, Y.-Y. (2014), “Predicting successful memes using network and community structure”, Proc. 8th AAAI Int. Conf. Weblogs Soc. Media, pp. 535-544. Yagan, O., Qian, D., Zhang, J. and Cochran, D. (2013), “Conjoining speeds up information diffusion in overlaying social-physical networks”, IEEE Journal on Selected Areas in Communications, Vol. 31 No. 6, pp. 1038-1048. Yang, J. and Leskovec, J. (2010), “Modeling information diffusion in implicit networks”, 2010 IEEE International Conference on Data Mining, pp. 599-608. Yu, W., Gao, C., Guojie, S. and Kunqing, X. (2010), “Community-based greedy algorithm for mining top- kinﬂuential nodes in mobile social networks”, Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ser. KDD ’10, ACM, New York, NY, pp. 1039-1048, doi: 10.1145/1835804.1835935. Yuan, C. and Ji, D. (2019), “Stochastic asymptotically stability of an information diffusion model with random perturbation in social network”, 2019 IEEE 8th Joint International Information Technology and Artiﬁcial Intelligence Conference (ITAIC), pp. 1916-1920. Further reading Wikipedia “Evolutionary game theory”, available at: https://en.wikipedia.org/wiki/Evolutionary_game_theory Wikipedia “Social network”, available at: http://en.wikipedia.org/wiki/Social_network Corresponding author Hangjing Zhang can be contacted at: zhanghangjing@std.uestc.edu.cn For instructions on how to order reprints of this article, please visit our website: www.emeraldgrouppublishing.com/licensing/reprints.htm Or contact us for further details: permissions@emeraldinsight.com

Journal

International Journal of Crowd Science – Emerald Publishing

Published: Mar 3, 2020

Keywords: Crowd behaviour analysis; Information diffusion; Evolutionary game theory

References

Information diffusion predictive model using radiation transfer

Alsuwaidan, L.; Ykhlef, M.
The role of social networks in information diffusion

Bakshy, E.; Rosenn, I.; Marlow, C.; Adamic, L.
Evolutionary information diffusion over heterogeneous social networks

Cao, X.; Chen, Y.; Jiang, C.; Ray Liu, K.J.
Machine learning based method to predict influence spread

Chejara, P.; WilfredGodfrey, W.
The spread of behavior in an online social network experiment

Damon, C.
Modeling complex social contagions in big data era

Ding, X.; Wu, Z.; Chen, W.; Liu, Y.; Xie, Y.; Cai, S.
Data never sleeps 7.0
Game theoretic analysis of a strategic model of competitive contagion and product adoption in social networks

Fazeli, A.; Jadbabaie, A.
Structure and dynamics of information pathways in online media

Gomez Rodriguez, M.; Leskovec, J.; Schölkopf, B.
Competitive contagion in networks

Goyal, S.; Kearns, M.
Information diffusion through blogspace

Gruhl, D.; Guha, R.; Liben-Nowell, D.; Tomkins, A.
Predicting information diffusion via matrix factorization based model

Hao, X.; Sheng, G.; Yu, Z.; Juncen, L.; Huacan, P.; Jun, G.
A distributed and privacy preserving algorithm for identifying information hubs in social networks

Ilyas, M.U.; Shafiq, M.Z.; Liu, A.X.; Radha, H.
Predicting the speed, scale, and range of information diffusion in twitter

Jiang, Y.; Scott, C.
Graphical evolutionary game for information diffusion over social networks

Jiang, C.; Chen, Y.; Liu, K.J.R.
Evolutionary dynamics of information diffusion over social networks

Jiang, C; Chen, Y.; Liu, K.J.R.
K-center: an approach on the multi-source identification of information diffusion

Jiang, J.; Wen, S.; Yu, S.; Xiang, Y.; Zhou, W.
Modeling of information diffusion based on network dimension-force

Jin-Lou, Z.; Zhi-bin, L.; Jian-Nan, Y.
Influential neighbours selection for information diffusion in online social networks

Kim, H.; Yoneki, E.
Extracting influential nodes for information diffusion on a social network

Kimura, M.; Saito, K.; Nakano, R.
Multiplex influence maximization in online social networks with heterogeneous diffusion models

Kuhnle, A.; Alim, M.A.; Li, X.; Zhang, H.; Thai, M.T.
A new correlation-based information diffusion prediction

Lee, J.-R.; Chung, -W.
Meme-tracking and the dynamics of the news cycle

Leskovec, J.; Backstrom, L.; Kleinberg, J.
Predicting trends in social networks via dynamic activeness model

Lin, S.; Kong, X.; Yu, P.S.
How much data is collected every minute of the day

Martin, N.
Blocking links to minimize contamination spread in a social network

Masahiro, K.; Kazumi, S.; Hiroshi, M.
Contagion

Morris, S.
A shapley value-based approach to discover influential nodes in social networks

Narayanam, R.; Narahari, Y.
The top 20 valuable facebook statistics c updated september 2019

Noyes, D.
The replicator equation on graphs

Ohtsukia, H.; Nowak, M.A.
Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs

Ohtsuki, H.; Nowak, M.A.; Pacheco, J.M.
Statistical mechanics of rumor spreading in network communities

Ostilli, M.; Yoneki, E.; Leung, I.X.; Mendes, J.F.; Lio, P.; Crowcroft, J.
Epidemic spreading in scale-free networks

Pastor-Satorras, R.; Vespignani, A.
Predicting information diffusion initiated from multiple sources in online social networks

Peng, C.; Xu, K.; Wang, F.; Wang, H.
Using early view patterns to predict the popularity of youtube videos

Pinto, H.; Almeida, J.M.; Gonçalves, M.A.
Modeling information propagation with survival theory

Rodriguez, M.; Leskovec, J.; Scholkopf, B.
Uncovering the structure and temporal dynamics of information propagation

Rodriguez, M.G.; Leskovec, J.; Balduzzi, D.; Schölkopf, B.
Finding k-most influential users in social networks for information diffusion based on network structure and different user behavioral patterns

Shahsavari, M.; Golpayegani, A.H.
Exploiting rank-learning models to predict the diffusion of preferences on social networks

Tsai, C.; Lou, J.; Lu, W.; Lin, S.
Analysis of influential features for information diffusion

Usui, S.; Toriumi, F.; Hirayama, T.; Mase, K.
Drimux: dynamic rumor influence minimization with user experience in social networks

Wang, B.; Chen, G.; Fu, L.; Song, L.; Wang, X.
Predicting successful memes using network and community structure

Weng, L.; Menczer, F.; Ahn, Y.-Y.
Conjoining speeds up information diffusion in overlaying social-physical networks

Yagan, O.; Qian, D.; Zhang, J.; Cochran, D.
Modeling information diffusion in implicit networks

Yang, J.; Leskovec, J.
Community-based greedy algorithm for mining top-k influential nodes in mobile social networks

Yu, W.; Gao, C.; Guojie, S.; Kunqing, X.
Stochastic asymptotically stability of an information diffusion model with random perturbation in social network

Yuan, C.; Ji, D.
Evolutionary game theory
Social network

Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Evolutionary information dynamics over social networks: a review

Evolutionary information dynamics over social networks: a review

Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Evolutionary information dynamics over social networks: a review

Evolutionary information dynamics over social networks: a review

References

Abstract

Journal

Recommended Articles

References

Our policy towards the use of cookies