Robustness in network community detection under links weights uncertainties

In network analysis, a community can be defined as a group of nodes of a network (or clusters) that are densely interconnected with each other but only sparsely connected with the rest of the network. Several algorithms have been used to obtain a convenient partition allowing extracting the communities in a given network, based on their topology and, possibly, the weights of links. These weights usually represent specific characteristics for example: distance, reactance, reliability. Even if the optimum partitions could be derived, there are uncertainties associated to the network parameters that affect the network partition. In this paper, the authors extend a previous approach for assessing the effects of weight uncertainties on community structures and propose a global approach for (a) understanding the global similarity among the partitions; (b) analyzing the robustness of the communities derived without uncertainty; and (c) quantifying the robustness of the inter-community links. To this aim an uncertainty propagation analysis, based on the Monte Carlo technique is proposed. The approach is illustrated through analyzing the topology of an electric power system. •Approach for analyzing the effect of uncertainties in the link weights of a network as a function of network similarity.•Global similarity between the original and the perturbed partitions of networks is evaluated.•Robustness of all of the original communities is quantified.•Robustness of all of the original inter-community links (ICL) is identified.•Use of a confidence level allows qualifying the communities or the ICL as robust.