← 研踪 PaperTrailarXiv:2611.16555 · v1
Similarity-Guided Optimization Strategies for Approximate Network Symmetry Detection
首次提交 2026-11-12 17:44
版本更新 2026-11-12 17:44
雷达观测 2026-11-13 14:15
摘要
Symmetry in complex networks is a structural property with broad implications for network function, dynamics, and robustness. While classical approaches rely on exact automorphisms and thus remain highly sensitive to small perturbations, recent work of Liu has introduced approximate formulations that relax the strict invariance condition and recast symmetry detection as an optimization problem over permutations. We investigate how node-level similarity information can be used to bias the search toward structurally plausible vertex correspondences, with network centralities serving as one interpretable instance. Building on this perspective, we adapt simulated annealing, genetic algorithms, tabu search, particle swarm optimization, differential evolution and the quadratic symmetry approximator to this problem, add similarity guidance to each, and introduce Bilinear Approximate Symmetry Inference (BASIN), which learns a soft assignment matrix via bilinear embeddings. Using a unified evaluation pipeline, we compare their guided and unguided variants, BASIN and a random baseline on four synthetic graph families, structural brain connectomes, and three empirical networks with known automorphism groups. Node-similarity guidance is decisive where a planted orbit exists that the unguided search misses, and algorithm-dependent elsewhere, on synthetic and empirical networks alike. Overall, tabu search achieves the strongest performance; its guided variant (SGTS) has the lowest median score among the guided variants in all 44 synthetic conditions, while BASIN is the better of the continuous relaxations on rewired lateral graphs. The effect of node-similarity guidance is therefore regime-dependent rather than uniformly positive.
作者备注：90 pages, 15 figures and 2 tables in the main text; supplementary material with 64 figures and 7 tables included
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v1 · 2026-11-12 17:44 · 最新观测版本
Similarity-Guided Optimization Strategies for Approximate Network Symmetry Detection
Symmetry in complex networks is a structural property with broad implications for network function, dynamics, and robustness. While classical approaches rely on exact automorphisms and thus remain highly sensitive to small perturbations, recent work of Liu has introduced approximate formulations that relax the strict invariance condition and recast symmetry detection as an optimization problem over permutations. We investigate how node-level similarity information can be used to bias the search toward structurally plausible vertex correspondences, with network centralities serving as one interpretable instance. Building on this perspective, we adapt simulated annealing, genetic algorithms, tabu search, particle swarm optimization, differential evolution and the quadratic symmetry approximator to this problem, add similarity guidance to each, and introduce Bilinear Approximate Symmetry Inference (BASIN), which learns a soft assignment matrix via bilinear embeddings. Using a unified evaluation pipeline, we compare their guided and unguided variants, BASIN and a random baseline on four synthetic graph families, structural brain connectomes, and three empirical networks with known automorphism groups. Node-similarity guidance is decisive where a planted orbit exists that the unguided search misses, and algorithm-dependent elsewhere, on synthetic and empirical networks alike. Overall, tabu search achieves the strongest performance; its guided variant (SGTS) has the lowest median score among the guided variants in all 44 synthetic conditions, while BASIN is the better of the continuous relaxations on rewired lateral graphs. The effect of node-similarity guidance is therefore regime-dependent rather than uniformly positive.
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