Detecting Functional Communities in Complex Networks

TL;DR

This paper introduces a functionally motivated community detection method based on maximizing eigenvalues related to synchronization and resilience, offering a new perspective beyond traditional structural modularity.

Contribution

It proposes a novel eigenvalue-based approach for identifying communities that are functionally cohesive, differing from and comparing to existing modularity methods.

Findings

The method effectively identifies communities aligned with network functions.

Eigenvalue-based partitions often outperform structural modularity in functional contexts.

In many cases, modularity approximates the functional communities despite not considering function explicitly.

Abstract

We consider an alternate definition of community structure that is functionally motivated. We define network community structure-based on the function the network system is intended to perform. In particular, as a specific example of this approach, we consider communities whose function is enhanced by the ability to synchronize and/or by resilience to node failures. Previous work has shown that, in many cases, the largest eigenvalue of the network's adjacency matrix controls the onset of both synchronization and percolation processes. Thus, for networks whose functional performance is dependent on these processes, we propose a method that divides a given network into communities based on maximizing a function of the largest eigenvalues of the adjacency matrices of the resulting communities. We also explore the differences between the partitions obtained by our method and the modularity approach (which is based solely on consideration of network structure). We do this for several different classes of networks. We find that, in many cases, modularity-based partitions do almost as well as our function-based method in finding functional communities, even though modularity does not specifically incorporate consideration of function.