Effects of multi-state links in network community detection

A community is defined as a group of nodes of a network that are densely interconnected with each other but only sparsely connected with the rest of the network. The set of communities (i.e., the network partition) and their inter-community links could be derived using special algorithms account for the topology of the network and, in certain cases, the possible weights associated to the links. In general, the set of weights represents some characteristic as capacity, flow and reliability, among others. The effects of considering weights could be translated to obtain a different partition. In many real situations, particularly when modeling infrastructure systems, networks must be modeled as multi-state networks (e.g., electric power networks). In such networks, each link is characterized by a vector of known random capacities (i.e., the weight on each link could vary according to a known probability distribution). In this paper a simple Monte Carlo approach is proposed to evaluate the effects of multi-state links on community detection as well as on the performance of the network. The approach is illustrated with the topology of an electric power system.