Measure of influences in social networks

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.