An indicator for community structure

TL;DR

This paper introduces an indicator that determines the potential existence of community structures in networks without requiring computationally intensive algorithms, helping to identify networks that lack such structures.

Contribution

The paper proposes a novel indicator to assess the presence of community structure in networks, enabling quick theoretical evaluation without complex computations.

Findings

The indicator can identify networks that cannot have community structures.

It provides a theoretical criterion to exclude networks lacking community organization.

The method reduces the need for costly community detection algorithms.

Abstract

An indicator for presence of community structure in networks is suggested. It allows one to check whether such structures can exist, in principle, in any particular network, without a need to apply computationally cost algorithms. In this way we exclude a large class of networks that do not possess any community structure.