Comparing signed networks through communicability embedding

Area of Science:

• Complex Systems Science
• Network Science
• Data Analysis

Background:

• Real-world complex systems often feature signed interactions (positive/negative links).
• Conventional network comparison methods struggle with the heterogeneity of signed networks.
• Existing methods fail to adequately capture the impact of positive and negative links on network structure.

Purpose of the Study:

• To introduce a new network comparison method, Signed Communicability Embedding (SCE), for signed complex networks.
• To develop a unified measure integrating topological structure and relation polarity.
• To address the limitations of conventional methods in handling signed interactions.

Main Methods:

• Utilized the matrix exponential of the signed adjacency matrix.
• Captured cumulative contributions of positive and negative walks across multiple scales.
• Quantified network dissimilarity using discrepancies in pairwise node distances within an embedding space.
• Incorporated a spectral correction strategy to mitigate scale-induced bias.

Main Results:

• SCE demonstrated stable and discriminative performance on diverse real-world signed networks.
• The method effectively captured structural shifts induced by negative edge changes.
• SCE disentangled differences arising from topology and sign configurations.
• Networks were organized into distinct structural regimes based on connectivity density, local closure, and signed interaction heterogeneity.

Conclusions:

• SCE provides a coherent and interpretable approach for network comparison in complex signed systems.
• The method successfully integrates topological structure and relation polarity into a unified measure.
• SCE offers improved analysis capabilities for networks with both positive and negative interactions.