Quantifying the resilience of community structures in networks

Many networks contain community structures, or collections of densely connected nodes with sparse connections to other dense groups in the network. Communities may coalesce for a number of reasons, including friendships in a social network, physical connections in an infrastructure network, or spatial distribution in a neighborhood. Several approaches have been proposed to identify communities and compare the partition of networks into communities. This work explores community structures from the perspective of their resilience, or their ability to withstand degradation in network performance and recover to a desired level of network performance. In this context, network performance is defined as the similarity of a network partition (or the characterization of the network into community structures) formed after the disconnection of one or more links to the initial partition. This work provides an approach to measure how the initial set of community structures survive after a disruption and how these structures return after restoration commences. The approach is illustrated with an electric power network case study.