Measure of influences in social networks

Abstract Society may be assumed to be a combination of several small networks. Naturally, an individual from one network is connected to several other networks (associated networks). The concept of associated networks is introduced here in a fuzzy environment. Although individuals of a given (focal) network are more likely to interact with others in the network, individuals from an associated network(s) also play an essential role in influencing decisions in the focal network. In this study, a measure of the influence of an individual (node) on/from individuals in the focal network and that in the context of associated networks have been developed using fuzzy systems. Mathematical formulations for the notion of the influence of a node have been developed based on the structure of a network. Also, fuzzy parameters that capture real-life situation-based characteristics (for example, characteristics of a connected associated network) have been included. Thus, the objective (structure-based) and subjective (using fuzzy membership parameters) nature of the network have been captured. We collected Facebook data to illustrate the proposed approach. We consider new features: (a) a fuzzy definition of centrality measures, (b) power measure, (c) notion of associated network and a measure for linking it to the main network, (d) in addition, we provide a mechanism ( through subjective parameters) to adapt our approach to a given situation, thus making our approach adaptable to a variety of applications. In this study, another application on the spreading of COVID19 affected regions has been discussed.

[1]  Ming Tang,et al.  Improving the accuracy of the k-shell method by removing redundant links: From a perspective of spreading dynamics , 2015, Scientific Reports.

[2]  F. Bass.  A new product growth model for consumer durables , 1976 .

[3]  Lada A. Adamic,et al.  Social influence and the diffusion of user-created content , 2009, EC '09.

[4]  S. Asch.  Effects of Group Pressure Upon the Modification and Distortion of Judgments , 1951 .

[5]  Gert Sabidussi,et al.  The centrality index of a graph , 1966 .

[6]  Alessandro Vespignani,et al.  Immunization of complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Madhumangal Pal,et al.  Fuzzy Planar Graphs , 2015, IEEE Transactions on Fuzzy Systems.

[8]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[9]  Sankar K. Pal,et al.  FGSN: Fuzzy Granular Social Networks - Model and applications , 2015, Inf. Sci..

[10]  Fereshteh-Azadi Parand,et al.  Combining fuzzy logic and eigenvector centrality measure in social network analysis , 2016 .

[11]  Mark S. Granovetter.  Threshold Models of Collective Behavior , 1978, American Journal of Sociology.

[12]  M. Newman,et al.  Finding community structure in networks using the eigenvectors of matrices. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Jinlong Zhang,et al.  Hybridizing Social Filtering for Recommender Systems , 2014 .

[14]  Filip Agneessens,et al.  Geodesic based centrality: Unifying the local and the global , 2017, Soc. Networks.

[15]  Mahdi Jalili,et al.  Identification of influential users in social network using gray wolf optimization algorithm , 2020, Expert Syst. Appl..

[16]  M. Blue,et al.  Unified approach to fuzzy graph problems , 2002, Fuzzy Sets Syst..

[17]  Ming Tang,et al.  Identify influential spreaders in complex networks, the role of neighborhood , 2015, ArXiv.

[18]  Ricardo Lopes de Andrade,et al.  P-means Centrality , 2019, Commun. Nonlinear Sci. Numer. Simul..

[19]  Frank M. Bass,et al.  A New Product Growth for Model Consumer Durables , 2004, Manag. Sci..

[20]  Mark S. Granovetter.  The Strength of Weak Ties , 1973, American Journal of Sociology.

[21]  Weijia Jia,et al.  Influence analysis in social networks: A survey , 2018, J. Netw. Comput. Appl..

[22]  Mark E. J. Newman.  A measure of betweenness centrality based on random walks , 2005, Soc. Networks.

[23]  Ron Shachar,et al.  Targeted advertising as a signal , 2009 .

[24]  Ahmad Zareie,et al.  EHC: Extended H-index Centrality measure for identification of users’ spreading influence in complex networks , 2019, Physica A: Statistical Mechanics and its Applications.

[25]  Madhumangal Pal,et al.  Study on centrality measures in social networks: a survey , 2018, Social Network Analysis and Mining.

[26]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[27]  Soumyadeep Debnath,et al.  Top-k Influential Nodes Identification Based on Activity Behaviors in Egocentric Online Social Networks , 2020 .