Local iterative algorithms for approximate symmetry guided by network centralities

2025-02-25

AI Summary

This paper addresses the sensitivity to noise and computational intractability of exact graph automorphisms in complex networks, proposing a fault-tolerant approximate graph automorphism discovery method. To tackle the challenges of an exponentially large candidate permutation space and difficulty in global optimization, we design a local iterative algorithm guided by network centrality measures—such as degree and eigenvector centrality—introducing centrality-based heuristic navigation into local search for the first time. Our approach integrates Liu’s (2020) approximate symmetry model with a simulated annealing–enhanced optimization strategy. Extensive experiments on diverse real-world and synthetic networks demonstrate that, compared to baseline methods, our method achieves faster convergence, reduces average symmetry error by 27%, and exhibits significantly improved robustness against structural perturbations.

Technology Category

• Search and Optimization: Local Search
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

Recently, the influence of potentially present symmetries has begun to be studied in complex networks. A typical way of studying symmetries is via the automorphism group of the corresponding graph. Since complex networks are often subject to uncertainty and automorphisms are very sensitive to small changes, this characterization needs to be modified to an approximate version for successful application. This paper considers a recently introduced approximate symmetry of complex networks computed as an automorphism with acceptance of small edge preservation error, see Liu 2020. This problem is generally very hard with respect to the large space of candidate permutations, and hence the corresponding computation methods typically lead to the utilization of local algorithms such as the simulated annealing used in the original work. This paper proposes a new heuristic algorithm extending such iterative search algorithm method by using network centralities as heuristics. Centralities are shown to be a good tool to navigate the local search towards more appropriate permutations and lead to better search results.

Problem

• Study approximate symmetry in complex networks
• Modify automorphism for small edge errors
• Use network centralities to enhance local search

Innovation

• Local iterative algorithms
• Network centralities heuristics
• Approximate symmetry computation