Statistical significance of communities in networks

TL;DR

This paper introduces a statistical measure to evaluate the significance of communities in networks, using Extreme and Order Statistics to compare real-world communities against random graph models.

Contribution

It proposes a novel method to quantify community significance based on probability distributions derived from Extreme and Order Statistics.

Findings

The method effectively assesses community significance in real-world networks.

It provides a probabilistic framework to distinguish meaningful communities from random structures.

The approach is validated on real-world network data.

Abstract

Nodes in real-world networks are usually organized in local modules. These groups, called communities, are intuitively defined as sub-graphs with a larger density of internal connections than of external links. In this work, we introduce a new measure aimed at quantifying the statistical significance of single communities. Extreme and Order Statistics are used to predict the statistics associated with individual clusters in random graphs. These distributions allows us to define one community significance as the probability that a generic clustering algorithm finds such a group in a random graph. The method is successfully applied in the case of real-world networks for the evaluation of the significance of their communities.