Network Structure Revealed by Short Cycles

TL;DR

This paper investigates how short cycles in complex networks can reveal community structures, using theoretical models and real-world data to identify subnetworks rich in cycles of length 3 to 5.

Contribution

It introduces a method to extract community-related subnetworks based on short cycle detection, linking local cycle patterns to global community organization.

Findings

Short cycles are indicative of community structure.

The method successfully identifies communities in both models and real networks.

Short cycle-based subnetworks highlight densely connected groups.

Abstract

This article explores the relationship between communities and short cycles in complex networks, based on the fact that nodes more densely connected amongst one another are more likely to be linked through short cycles. By identifying combinations of 3-, 4- and 5-edge-cycles, a subnetwork is obtained which contains only those nodes and links belonging to such cycles, which can then be used to highlight community structure. Examples are shown using a theoretical model (Sznajd networks) and a real-world network (NCAA football).