Challenges of Generating Structurally Diverse Graphs

TL;DR

This paper addresses the challenge of generating a set of structurally diverse graphs, proposing new algorithms and analysis methods to improve diversity and understand graph distance properties.

Contribution

It introduces a formal definition of graph diversity, compares multiple algorithms for generating diverse graphs, and analyzes how different measures affect graph properties.

Findings

Significant improvement in diversity over basic random graph models

Different diversity measures lead to graphs with distinct structural properties

Enhanced understanding of graph distances through generated graph analysis

Abstract

For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the problem of generating structurally diverse graphs has not been explored in the literature. In this paper, we fill this gap. First, we discuss how to define diversity for a set of graphs, why this task is non-trivial, and how one can choose a proper diversity measure. Then, for a given diversity measure, we propose and compare several algorithms optimizing it: we consider approaches based on standard random graph models, local graph optimization, genetic algorithms, and neural generative models. We show that it is possible to significantly improve diversity over basic random graph generators. Additionally, our analysis of generated graphs allows us to better understand the properties of graph distances: depending on which diversity measure is used for optimization, the obtained graphs may possess very different structural properties which gives a better understanding of the graph distance underlying the diversity measure.