Gravity-Based Community Vulnerability Evaluation Model in Social Networks: GBCVE

The usage of social media around the world is ever-increasing. Social media statistics from 2019 show that there are 3.5 billion social media users worldwide. However, the existence of community structure renders the network vulnerable to attacks and large-scale losses. How does one comprehensively consider the multiple information sources and effectively evaluate the vulnerability of the community? To answer this question, we design a gravity-based community vulnerability evaluation (GBCVE) model for multiple information considerations. Specifically, we construct the community network by the Jensen-Shannon divergence and log-sigmoid transition function to show the relationship between communities. The number of edges inside community and outside of each community, as well as the gravity index are the three important factors used in this model for evaluating the community vulnerability. These three factors correspond to the interior information of the community, small-scale interaction relationship, and large-scale interaction relationship, respectively. A fuzzy ranking algorithm is then used to describe the vulnerability relationship between different communities, and the sensitivity of different weighting parameters is then analyzed by Sobol' indices. We validate and demonstrate the applicability of our proposed community vulnerability evaluation method via three real-world complex network test examples. Our proposed model can be applied to find vulnerable components in a network to mitigate the influence of public opinions or natural disasters in real time. The community vulnerability evaluation results from our proposed model are expected to shed light on other properties of communities within social networks and have real-world applications across network science.