|InterJournal Complex Systems, 1765
|Manuscript Number: |
Submission Date: 2006
|On Motif Statistics in Symmetric Networks|
In recent years, networks derived from complex systems have been studied not just in terms of global properties like degree distributions, but also in terms of motifs, small subgraphs whose appearances can be examined statistically. Motifs which occur more often than chance predicts are often presumed to indicate some feature of local structure which is preferred for biological, physical or geometrical reasons. I test a claim made in R. Milo et al., Science 303 (5 March 2004) to the effect that protein structures can be approached in this way, studying not three proteins but a set of 830. Overall, the general claim of the earlier paper is borne out: the spatial distribution of secondary-structure elements can be roughly understood as a geometrically constrained network. Structures of individual proteins are reflected in the clustering coefficients of the networks derived from the protein geometries. The nature of geometrical constraints on network topology raises issues of symmetry, which also affect the ways the presence of multiple protein domains can skew motif statistics.
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