Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2003-06-24
Phys. Rev. E 71, 016110 (2005)
Physics
Condensed Matter
Disordered Systems and Neural Networks
19 pages, 12 figures
Scientific paper
10.1103/PhysRevE.71.016110
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.
Koytcheff Robin
Middendorf Manuel
Wiggins Chris
Ziv Etay
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