Omega-N: Interpretable Structural Node Descriptors and Their Applicability Domain

Abstract:A composite structural index summarises a network in one number; for a triangle-based index it is spectrally redundant: Tr(A^3) is the third moment of the adjacency spectrum. The non-redundant content sits one level down, in diag(A^3), which depends on eigenvectors and is not spectrally determined. A corollary in the theory paper for this index family stated that, and predicted: the global scalar should tie sharpened spectral baselines rather than beat them, while the node-wise attribution should do better where the number of structural epicentres is unknown. This paper tests it. We construct Omega-N by localizing each of the four factors. The direct localization is badly conditioned; two corrections from published practice fix it, a configuration-null excess for every local factor and a personalized-PageRank neighbourhood at several scales, giving ten interpretable features per node from the graph alone, with no attributes, training or embeddings. Against a recursive feature engine at five levels of recursion, Omega-N wins on one and ties on four of six in-domain node-classification evaluations, with ten features against up to 252. Two statistics computed from the graph and labels, not from performance, partition the eight benchmarks without error, and the two they exclude are the two it loses. The strongest application is drug-target prioritisation on protein interaction networks: +0.073 to +0.144 AUPRC over a centrality battery across four constructions, replicated on an independent AP-MS network and label source, surviving three bias controls (degree-matched, ten repetitions: +0.1047 and +0.1030, both 10/10, p=0.00195). The clearest negative sits in the same application: adding Omega-N to centralities plus Node2Vec changes nothing (+0.0014, p=0.31). The claim is narrow: ten interpretable features

18 pages, 3 figures. Reference implementation, notebooks and data-preparation scripts at this https URL

Social and Information Networks (cs.SI); Machine Learning (cs.LG); Physics and Society (physics.soc-ph); Molecular Networks (q-bio.MN)

arXiv:2609.01633 [cs.SI]

(or arXiv:2609.01633v1 [cs.SI] for this version)

https://doi.org/10.48550/arXiv.2609.01633 Focus to learn more arXiv-issued DOI via DataCite

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