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Generalised network clustering and its dynamical implications

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House, Thomas A.. (2010) Generalised network clustering and its dynamical implications. Advances in Complex Systems, Vol.13 (No.3). pp. 281-291. ISSN 0219-5259

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Official URL: http://dx.doi.org/10.1142/S0219525910002645

Abstract

A parametrization of generalised network clustering, in the form of four-motif prevalences, is presented. This involves three real parameters that are conditional on one-, two- and three-motif prevalences. Interpretations of these real parameters are presented that motivate a set of rewiring schemes to create appropriately clustered networks. Finally, the dynamical implications of higher order structure, as parameterised, for a contact process are considered.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Cluster analysis, System analysis
Journal or Publication Title:	Advances in Complex Systems
Publisher:	World Scientific Publishing Company PTE Ltd
ISSN:	0219-5259
Date:	June 2010
Volume:	Vol.13
Number:	No.3
Number of Pages:	11
Page Range:	pp. 281-291
Identification Number:	10.1142/S0219525910002645
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), Medical Research Council (Great Britain) (MRC)
Grant number:	G0701256 (MRC), EP/H016139/1 (EPSRC)
References:	[1] Bansal, S., Khandelwal, S., and Meyers, L. A., Exploring biological network structure with clustered random networks, BMC Bioinformatics 10 (2009) 405. [2] Green, D. M. and Kiss, I. Z., Large-scale properties of clustered networks: Implications for disease dynamics, Journal of Biological Dynamics (2010). [3] House, T., Davies, G., Danon, L., and Keeling, M. J., A motif-based approach to network epidemics, Bulletin of Mathematical Biology 71 (2009) 1693–1706. [4] House, T. and Keeling, M. J., The impact of contact tracing in clustered populations, PLoS Computational Biology 6 (2010) e1000721. [5] Keeling, M. J. and Rohani, P., Modeling Infectious Diseases in Humans and Animals (Princeton University Press, 2007). [6] Kiss, I. Z. and Green, D. M., Comment on “properties of highly clustered networks”, Physical Review E 78 (2008) 048101. [7] Milo, R., Superfamilies of evolved and designed networks, Science 303 (2004) 1538–1542. [8] Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., and Alon, U., Network motifs: simple building blocks of complex networks, Science 298 (2002) 824–7. [9] Newman, M. E. J., The structure and function of complex networks, SIAM Review 45 (2003) 167–256. [10] Strogatz, S. H., Exploring complex networks, Nature 410 (2001) 268–276. [11] Wasserman, S. and Faust, K., Social Network Analysis: Methods and Ap- plications (Cambridge University Press, 1994). [12] Watts, D. J., Six degrees: The science of a connected age (WW Norton, 2003). [13] Watts, D. J. and Strogatz, S. H., Collective dynamics of ‘small-world’ networks, Nature 393 (1998) 440–442.
URI:	http://wrap.warwick.ac.uk/id/eprint/5586