A series of real networks invariants

2026-01-05

arXiv.org

AI Summary

This study addresses the challenge of effectively distinguishing structural characteristics between real-world and synthetic networks. To this end, the authors propose a family of novel centrality measures based on the graph Laplacian matrix, generalizing both degree centrality and κ-centrality. The node distributions of these measures follow an exponential family, degenerating to a power-law distribution when \( j = 0 \). By integrating spectral analysis with centrality quantification, the approach reveals stable distribution patterns in empirical networks, while exhibiting marked deviations in canonical synthetic networks. Experimental results demonstrate that the proposed metrics successfully capture topological invariants inherent to real networks, offering strong discriminative power and establishing a new theoretical framework for validating network authenticity.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

In this article we propose a generalization of two known invariants of real networks: degree and ksi-centrality. More precisely, we found a series of centralities based on Laplacian matrix, that have exponential distributions (power-law for the case $j = 0$) for real networks and different distributions for artificial ones.

Problem

• network invariants
• degree
• centrality
• real networks
• Laplacian matrix

Innovation

• Laplacian-based centrality
• network invariants
• exponential distribution
• power-law distribution
• real networks