Vulnerability metrics and analysis for communities in complex networks

This paper applies the problem of community detection in complex networks to identify sets of network elements that are critical to the connectivity of the network and its communities. Specifically, the paper defines a vulnerability set and value for each of the communities in a complex network. Also, for each community it identifies a value of relative vulnerability in comparison with the remaining communities. The approach allows to visualize/identify the critical elements of a complex network. This is an important first step for many recent problems arising in social networks, critical infrastructures and homeland security. By identifying these elements one can prioritize resource allocation to protect, interdict or improve performance in these types of systems. The sets and metrics introduced are illustrated with numerous examples and discussions. Based on the analysis of the examples the manuscript provides an intuitive description of a community's presence in the interior or periphery of a network.