Community Detection in Directed Weighted Networks using Voronoi Partitioning

Abstract

Community detection is a ubiquitous problem in applied network analysis, yet efficient techniques do not yet exist for all types of network data. Most techniques have been developed for undirected graphs, and very few exist that handle directed and weighted networks effectively. Here we present such an algorithm based on Voronoi partitionings. As an added benefit, this method can directly employ edge weights that represent lengths, in contrast to algorithms that operate with connection strengths, requiring ad-hoc transformations of length data. We demonstrate the method on inter-areal brain connectivity, air transportation networks, as well as on randomly generated benchmark networks. The algorithm can handle dense graphs where weights are the main factor determining communities. The hierarchical structure of networks can also be detected, as shown for the brain. Its time efficiency is comparable with other state-of-the-art algorithms, the most costly part being Dijkstra's shortest paths algorithm.