Comparing signed networks through communicability embedding.

Abstract

Network comparison plays a central role in characterizing structural differences and cross-network correlations in complex systems. In many real-world settings, however, interactions are inherently signed, with positive and negative links altering both connection semantics and structural organization. This challenges conventional comparison methods built upon unsigned assumptions, which are unable to adequately capture such heterogeneity. To address this limitation, we introduce a network comparison method based on Signed Communicability Embedding (SCE). SCE employs the matrix exponential of the signed adjacency matrix to capture the cumulative contributions of positive and negative walks across multiple scales. Network-level dissimilarity is then quantified through discrepancies in pairwise node distances within the resulting embedding space, thereby integrating topological structure and relation polarity into a unified measure. To further ensure consistency across networks, a spectral correction strategy is incorporated to mitigate scale-induced bias. Extensive experiments on diverse real-world signed networks show that SCE yields stable and discriminative performance under a variety of perturbation scenarios, particularly in capturing structural shifts induced by negative edge changes. Additional analyses based on null models and network clustering further show that SCE not only disentangles differences arising from topology and sign configurations but also organizes networks into distinct structural regimes, reflecting variations in connectivity density, local closure, and signed interaction heterogeneity. Overall, SCE provides a coherent and interpretable approach to network comparison in complex signed systems.