Finding role communities in directed networks using Role-Based Similarity, Markov Stability and the Relaxed Minimum Spanning Tree

TL;DR

This paper introduces a novel framework combining Role-Based Similarity, Relaxed Minimum Spanning Tree, and Markov Stability to identify role communities in directed networks, demonstrated on biological and synthetic examples.

Contribution

It develops an integrated method for role community detection in directed networks using flow-based similarity and multiscale clustering techniques.

Findings

Successfully identified role communities in biological networks

Effectively distinguished roles in synthetic directed networks

Provided a scalable approach for multiscale role detection

Abstract

We present a framework to cluster nodes in directed networks according to their roles by combining Role-Based Similarity (RBS) and Markov Stability, two techniques based on flows. First we compute the RBS matrix, which contains the pairwise similarities between nodes according to the scaled number of in- and out-directed paths of different lengths. The weighted RBS similarity matrix is then transformed into an undirected similarity network using the Relaxed Minimum-Spanning Tree (RMST) algorithm, which uses the geometric structure of the RBS matrix to unblur the network, such that edges between nodes with high, direct RBS are preserved. Finally, we partition the RMST similarity network into role-communities of nodes at all scales using Markov Stability to find a robust set of roles in the network. We showcase our framework through a biological and a man-made network.