Spatial correlations in attribute communities

TL;DR

This paper investigates how correlations between spatial location and node attributes affect community detection in spatial networks, revealing that ignoring these correlations can lead to significant detection failures.

Contribution

It introduces a simple model incorporating space-attribute correlations and analyzes their impact on various community detection methods in spatial networks.

Findings

Strong space-attribute correlations hinder community detection accuracy.

Removing spatial components can cause missed community structures.

Detectability transitions depend on the dominance of space or attributes.

Abstract

Community detection is an important tool for exploring and classifying the properties of large complex networks and should be of great help for spatial networks. Indeed, in addition to their location, nodes in spatial networks can have attributes such as the language for individuals, or any other socio-economical feature that we would like to identify in communities. We discuss in this paper a crucial aspect which was not considered in previous studies which is the possible existence of correlations between space and attributes. Introducing a simple toy model in which both space and node attributes are considered, we discuss the effect of space-attribute correlations on the results of various community detection methods proposed for spatial networks in this paper and in previous studies. When space is irrelevant, our model is equivalent to the stochastic block model which has been shown to display a detectability-non detectability transition. In the regime where space dominates the link formation process, most methods can fail to recover the communities, an effect which is particularly marked when space-attributes correlations are strong. In this latter case, community detection methods which remove the spatial component of the network can miss a large part of the community structure and can lead to incorrect results.