Local network evolution rules drive shortest path multiplicity

2026-05-24

AI Summary

High shortest-path multiplicity is a ubiquitous yet poorly understood feature of real-world complex networks. This study addresses its origin by constructing network models through numerical simulations based solely on local evolutionary rules. The work demonstrates for the first time that such high path multiplicity emerges naturally from purely local connection mechanisms and is intrinsically linked to community structure. Remarkably, networks generated under these local rules not only reproduce the observed levels of shortest-path multiplicity found in empirical networks but also exhibit community organization closely matching real-world data. These findings establish a theoretical bridge among local dynamical processes, shortest-path multiplicity, and modular architecture, revealing that global topological features can arise without centralized design or global information.

Abstract

The shortest path multiplicity is an important metric of complex networks. The shortest path multiplicity of real networks is high and it correlates with their community structure. Since local network evolution induces network communities, it is possible that a high shortest path multiplicity is the natural expectation of local evolution rules. Here I demonstrate, by means of numerical simulations, that this is indeed the case.

Problem

• shortest path multiplicity
• complex networks
• local network evolution
• community structure

Innovation

• local network evolution
• shortest path multiplicity
• community structure
• complex networks
• numerical simulations