Graph clustering via generalized colorings

TL;DR

This paper introduces a novel graph clustering method based on generalized colorings, focusing on the inter-cluster edge structure, inspired by ecological and economic network observations.

Contribution

It presents a new approach to graph clustering using generalized colorings and chromatic numbers, emphasizing inter-cluster edge structures rather than density.

Findings

Develops a mathematical framework for generalized graph colorings

Analyzes chromatic numbers related to cluster structures

Provides insights into network structures in ecology and economics

Abstract

We propose a new approach for defining and searching clusters in graphs that represent real technological or transaction networks. In contrast to the standard way of finding dense parts of a graph, we concentrate on the structure of edges between the clusters, as it is motivated by some earlier observations, e.g. in the structure of networks in ecology and economics and by applications of discrete tomography. Mathematically special colorings and chromatic numbers of graphs are studied.