Challenges of Generating Structurally Diverse Graphs
This addresses a gap in the literature for generating diverse graphs, which is useful for researchers and practitioners in graph-related fields, but it is incremental as it builds on existing methods.
The paper tackles the problem of generating structurally diverse graphs, which is essential for testing graph algorithms, by proposing and comparing several algorithms to optimize diversity measures, showing significant improvements over basic random graph generators.
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.