Measuring the vulnerability of community structure in complex networks

Highlights: • A quantitative metric is developed to measure the vulnerability of community structure. • Both internal and external connectivity characteristics of the community are considered in the developed metric. • The proposed metric is effective in distinguishing the vulnerability level of community structures in a variety of networks. This paper develops a quantitative method to measure the vulnerability of community structure with emphasis on both internal and external connectivity characteristics of the community. In particular, the number of links between communities and the strength of links connecting two communities are considered as external factors, while the connection density, the degree of gateway nodes, as well as the strength of links within each community are treated as internal factors. A non-linear weighted function is used to combine the internal factors with external factors. Then the developed method is used to illustrate the vulnerability analysis of community structure of a power transmission grid, a karate club network, and an air transportation network. The results reveal that the proposed measure is effective in differentiating the vulnerability level of community structure in a variety of networks.