# Stochastic graph Voronoi tessellation reveals community structure

## TL;DR

This paper introduces a novel stochastic Voronoi-based method for detecting community structures in networks by analyzing the probability of node pairs sharing the same Voronoi cell, providing global network insights.

## Contribution

It defines the Voronoi cohesion measure and explores its mathematical properties and applications, especially for community detection in complex networks.

## Key findings

- Voronoi cohesion effectively captures community structure
- The method provides global context information not available in traditional measures
- Potential limitations and applications are discussed

## Abstract

Given a network, the statistical ensemble of its graph-Voronoi diagrams with randomly chosen cell centers exhibits properties convertible into information on the network's large scale structures. We define a node-pair level measure called {\it Voronoi cohesion} which describes the probability for sharing the same Voronoi cell, when randomly choosing $g$ centers in the network. This measure provides information based on the global context (the network in its entirety) a type of information that is not carried by other similarity measures. We explore the mathematical background of this phenomenon and several of its potential applications. A special focus is laid on the possibilities and limitations pertaining to the exploitation of the phenomenon for community detection purposes.