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Systematic identification of statistically significant network measures

Etay Ziv·Robin Koytcheff·Manuel Middendorf·Chris Wiggins
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Abstract

We present a novel graph embedding space (i.e., a set of measures on graphs) for performing statistical analyses of networks. Key improvements over existing approaches include discovery of "motif-hubs" (multiple overlapping significant subgraphs), computational efficiency relative to subgraph census, and flexibility (the method is easily generalizable to weighted and signed graphs). The embedding space is based on {\it scalars}, functionals of the adjacency matrix representing the network. {\it Scalars} are global, involving all nodes; although they can be related to subgraph enumeration, there is not a one-to-one mapping between scalars and subgraphs. Improvements in network randomization and significance testing--we learn the distribution rather than assuming gaussianity--are also presented. The resulting algorithm establishes a systematic approach to the identification of the most significant scalars and suggests machine-learning techniques for network classification.

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Etay Ziv, Robin Koytcheff, Manuel Middendorf, Chris Wiggins. 2005-01-27. Systematic identification of statistically significant network measures. https://doi.org/10.1103/physreve.71.016110

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