Efficient community detection of network flows for varying Markov times and bipartite networks

TL;DR

This paper introduces an efficient method for community detection in network flows that operates at various Markov times without network reconstruction, applicable to large and bipartite networks.

Contribution

It presents a novel approach leveraging the map equation to analyze networks at different timescales efficiently, avoiding costly network reconstructions and bipartite projections.

Findings

Enables scalable community detection across multiple Markov times.

Eliminates the need for network reconstruction in flow analysis.

Avoids expensive bipartite network projections.

Abstract

Community detection of network flows conventionally assumes one-step dynamics on the links. For sparse networks and interest in large-scale structures, longer timescales may be more appropriate. Oppositely, for large networks and interest in small-scale structures, shorter timescales may be better. However, current methods for analyzing networks at different timescales require expensive and often infeasible network reconstructions. To overcome this problem, we introduce a method that takes advantage of the inner-workings of the map equation and evades the reconstruction step. This makes it possible to efficiently analyze large networks at different Markov times with no extra overhead cost. The method also evades the costly unipartite projection for identifying flow modules in bipartite networks.