Line Graph for Weighted Networks toward Overlapping Community Discovery

Abstract

We propose generalized line graph for weighted networks toward overlapping community discovery from the networks. Community discovery from a network has often been conducted by assigning each node in a network only to one community. However, in real world networks, a node (e.g., user) might belong to several communities. For undirected networks without self-loops, we propose to generalize line graph by defining the weights in the line graph based on the weights in the original network. Based on the line graph representation, a node can be assigned to more than one community by assigning the links adjacent to the node to the corresponding communities. Various properties of the proposed generalized line graph are clarified, and the properties indicate that our proposal is a natural extension of the conventional line graph. Preliminary experiments are conducted over several real-world networks, and the results indicate that the proposed generalized line graph can improve the quality of the discovered overlapping communities.