Efficient Graph Similarity Assessment Method Based on Vectors of Topological Indices

Measuring similarity between complex objects is a fundamental task in many scientific fields. When objects are represented as graphs, graph similarity/distance measures offer a powerful framework for quantifying structural resemblance. Those comparative measures play a key role in domains such as network science, chemoinformatics, and social network analysis. While methods like graph edit distance and graph kernels are widely used, they can be computationally intensive or fail to capture fine structural variations, since they require graphs without any structural uncertainty. Another class of methods is based on using topological indices to encode structural information of the graphs, followed by the application of distance or similarity measures for real numbers to obtain corresponding graph-level metrics. In this paper, we introduce a novel class of distance/similarity measures which are based on multiple topological indices. In many cases, they can be computed in polynomial time, which makes our method computationally efficient in practice. We demonstrate its effectiveness through comparisons and show that it captures subtle structural information meaningfully. Additionally, we explore its applicability in two domains: analyzing random graph models in network theory and assessing molecular similarity among isomers in chemoinformatics. These preliminary results suggest that our approach holds promise for graph comparison across disciplines.