Evolutionary Algorithms for Generating Graphs Matching Desired Laplacian Spectra

TL;DR

This paper introduces an evolutionary algorithm that generates diverse graphs matching specified Laplacian spectra, enabling control over high-level graph properties.

Contribution

A novel evolutionary method utilizing Laplacian spectra as a fitness function to produce graphs with desired spectral and structural characteristics.

Findings

Successfully generates graphs across various classes and spectra.

Produces graphs with targeted spectral properties and diverse structural metrics.

Demonstrates effectiveness in controlling high-level graph features.

Abstract

Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and configuration. However, constructing graphs that preserve high-level properties across a broad range of graph classes remains a challenging problem. We present a novel evolutionary approach to evolve graphs based on the Laplacian graph spectra descriptor. This descriptor can be used as part of a fitness function to evaluate graphs according to their desired high-level properties. Our evolutionary algorithm evolves graphs towards this descriptor in order to obtain graphs having properties that are consistent with it but are different from each other in terms of non-spectral graph metrics, such as path length, clustering coefficient and betweenness centrality. Our experimental results show that our approach is successful for different classes of graphs and a wide range of Laplacian graph spectra.