The vulnerability of communities in complex networks: An entropy approach

Measuring the vulnerability of communities in complex networks has become an important topic in the research of complex systems. Numerous existing vulnerability measures have been proposed to solve such a problem, however, most of these methods have their own shortcomings and limitations. Therefore, a new entropy-based approach is proposed in this paper to address such a problem. This measure combines the internal factors and external factors for each community which can give the quantitative description of the community vulnerability. The internal factors contain the complexity degree of the community and the number of edges inside the community, and the external factors contain the similarity degree between the chosen community and other communities and the number of edges outside the community. Considering the community vulnerability from the perspective of entropy provides a new solution to such a problem. Due to the sufficient consideration of community information, more reasonable vulnerability result can be obtained. In order to show the performance and effectiveness of this proposed method, one example network and four real-world complex networks are used to compare with some exiting methods, and the sensitivity of weight factors is analyzed by Sobol' indices. The experiment results demonstrate the reasonableness and superiority of this proposed method.