title: Motif-role-fingerprints: the building-blocks of motifs, clustering-coefficients and transitivities in directed networks.
abstract: Complex networks are frequently characterized by metrics for which particular subgraphs are counted. One statistic from this category, which we refer to as motif-role fingerprints, differs from global subgraph counts in that the number of subgraphs in which each node participates is counted. As with global subgraph counts, it can be important to distinguish between motif-role fingerprints that are 'structural' (induced subgraphs) and 'functional' (partial subgraphs). Here we show mathematically that a vector of all functional motif-role fingerprints can readily be obtained from an arbitrary directed adjacency matrix, and then converted to structural motif-role fingerprints by multiplying that vector by a specific invertible conversion matrix. This result demonstrates that a unique structural motif-role fingerprint exists for any given functional motif-role fingerprint. We demonstrate a similar result for the cases of functional and structural motif-fingerprints without node roles, and global subgraph counts that form the basis of standard motif analysis. We also explicitly highlight that motif-role fingerprints are elemental to several popular metrics for quantifying the subgraph structure of directed complex networks, including motif distributions, directed clustering coefficient, and transitivity. The relationships between each of these metrics and motif-role fingerprints also suggest new subtypes of directed clustering coefficients and transitivities. Our results have potential utility in analyzing directed synaptic networks constructed from neuronal connectome data, such as in terms of centrality. Other potential applications include anomaly detection in networks, identification of similar networks and identification of similar nodes within networks. Matlab code for calculating all stated metrics following calculation of functional motif-role fingerprints is provided as S1 Matlab File.
authors.affiliation: Computational and Theoretical Neuroscience Laboratory, Institute for Telecommunications Research, University of South Australia, Mawson Lakes, South Australia, Australia; Department of Psychology and Brain Research Centre, University of British Columbia, Vancouver, British Columbia, Canada.
authors.forename: Mark D
authors.initials: MD
authors.lastname: McDonnell
authors.affiliation: California Institute of Telecommunications and Information Technology (Calit2), University of California Irvine, Irvine, California, United States of America.
authors.forename: Ömer Nebil
authors.initials: ÖN
authors.lastname: Yaveroğlu
authors.affiliation: Computational and Theoretical Neuroscience Laboratory, Institute for Telecommunications Research, University of South Australia, Mawson Lakes, South Australia, Australia.
authors.forename: Brett A
authors.initials: BA
authors.lastname: Schmerl
authors.affiliation: Computational and Theoretical Neuroscience Laboratory, Institute for Telecommunications Research, University of South Australia, Mawson Lakes, South Australia, Australia.
authors.forename: Nicolangelo
authors.initials: N
authors.lastname: Iannella
authors.affiliation: Department of Psychology and Brain Research Centre, University of British Columbia, Vancouver, British Columbia, Canada.
authors.forename: Lawrence M
authors.initials: LM
authors.lastname: Ward
mesh_terms: D000465:Algorithms; D000818:Animals; D017173:Caenorhabditis elegans / Q000235:genetics*; D016000:Cluster Analysis; D019295:Computational Biology; D003198:Computer Simulation; D053263:Gene Regulatory Networks; D008954:Models, Biological; D009434:Neural Pathways; D009474:Neurons / Q000378:metabolism*; D025941:Protein Interaction Mapping