Baskerville, Paczuski (2006)

Authors: Kim Baskerville and Maya Paczuski
Published in: Physical Review E 74, 051903 (November 3, 2006)
More: PDF | arXiv

A new heuristic based on vertex invariants is developed to rapidly distinguish non-isomorphic graphs to a desired level of accuracy. The method is applied to sample subgraphs from an E.coli protein interaction network, and as a probe for discovery of extended motifs. The network's structure is described using statistical properties of its N-node subgraphs for N ? 14. The Zipf plots for subgraph occurrences are robust power laws that do not change when rewiring the network while fixing the degree sequence - although the specific subgraphs may exchange ranks. However the exponent depends on N. The study of larger subgraphs highlights some striking patterns for various N. Motifs, or connected pieces that are over-abundant in the ensemble of subgraphs, have more edges, for a given number of nodes, than antimotifs and generally display a bipartite structure or tend towards a complete graph. In contrast, antimotifs, which are under-abundant connected pieces, are mostly trees or contain at most a single, small loop. The extension to directed graphs is straightforward.

@article{baskerville2006sea,
title={{Subgraph ensembles and motif discovery using an alternative heuristic for graph isomorphism}},
author={Baskerville, K. and Paczuski, M.},
journal={Physical Review E},
volume={74},
number={5},
pages={51903},
year={2006},
publisher={APS}
}