A distribution-based framework for network similarity assessment

Assessing structural similarity between complex systems represented as networks is a fundamental challenge across many disciplines. Existing methods range from exact graph matching to inexact approaches such as graph edit distance, graph kernels, and topological index–based comparisons. In this work, we introduce a new distribution-based framework for network comparison. Each network is represented by its degree and distance distributions, which capture key structural features in probabilistic form. These distributions are compared using the Jensen–Shannon and Hellinger distance metrics. We further combine the degree- and distance-based dissimilarity measures into a unified similarity measure that captures complementary aspects of network structures. Moreover, we analyze its behavior on structured network families and demonstrate its applicability to both random and real-world networks, including molecular similarity assessment.