# Community structure unveils the path multiplicity in complex networks

## TL;DR

This paper shows that community structures in networks strongly influence the number of shortest paths between nodes.

## Contribution

The study introduces relative path multiplicity and links community structure as a key driver of path multiplicity.

## Key findings

- Community structure is more strongly correlated with path multiplicity than other network metrics.
- Targeted edge-rewiring experiments confirm the link between community structure and path multiplicity.
- A tribal-structure-based model reproduces real-world network phenomena.

## Abstract

Networks with complex topologies describe numerous natural and social systems. Recent studies on path multiplicity have shown strong heterogeneity in shortest paths between node pairs in real-world networks. However, the mechanism underlying this phenomenon remains unexplored. Here, we reveal that community structure is a key factor shaping path multiplicity. To explore the intrinsic factors that influence path multiplicity, we first introduce the concept of relative path multiplicity and find that community structure is more strongly correlated with path multiplicity than other network metrics. Through targeted edge-rewiring experiments, we verify the link between path multiplicity and community structure. The underlying mechanism can be interpreted as an interface-driven effect that sharply increases the number of shortest paths. Inspired by these findings, we propose a tribal-structure-based network model that reproduces phenomena observed in real-world networks. Our work enhances the understanding of network organization, with potential applications in network design and optimization.

Recent studies on path multiplicity have shown strong heterogeneity in shortest paths between node pairs in real-world networks. Here, authors reveal that community structure is a key factor shaping path multiplicity.