Evolutionary Algorithms for Generating Graphs Matching Desired Laplacian Spectra

2026-03-30

AI Summary

This work addresses the challenge of generating graphs that match a target Laplacian spectrum while exhibiting diverse structural characteristics—such as path lengths and clustering coefficients—which is crucial for graph modeling and algorithm configuration. The authors propose a novel evolutionary algorithm that, for the first time, employs the Laplacian spectrum as the fitness function to guide population evolution. By integrating tailored graph mutation operators, the method preserves structural diversity while accurately matching the desired spectral properties. Experimental results demonstrate that the approach efficiently produces spectrally consistent yet structurally varied graphs across a wide range of graph types and spectral targets, confirming its effectiveness and broad applicability.

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.

Problem

• graph generation
• Laplacian spectra
• graph properties
• evolutionary algorithms
• spectral graph theory

Innovation

• Evolutionary Algorithms
• Graph Generation
• Laplacian Spectra
• Fitness Function
• Graph Diversity