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A clustering coefficient for complete weighted networks

Published online by Cambridge University Press:  09 January 2015

MICHAEL P. MCASSEY  and
FETSJE BIJMA
MICHAEL P. MCASSEY
Affiliation:
Department of Mathetmatics, VU University Amsterdam, Amsterdam, the Netherlands (email: [email protected], [email protected])
FETSJE BIJMA
Affiliation:
Department of Mathetmatics, VU University Amsterdam, Amsterdam, the Netherlands (email: [email protected], [email protected])
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Abstract

The clustering coefficient is typically used as a measure of the prevalence of node clusters in a network. Various definitions for this measure have been proposed for the cases of networks having weighted edges which may or not be directed. However, these techniques consistently assume that only a subset of all possible edges is present in the network, whereas there are weighted networks of interest in which all possible edges are present, that is, complete weighted networks. For this situation, the concept of clustering is redefined, and computational techniques are presented for computing an associated clustering coefficient for complete weighted undirected or directed networks. The performance of this new definition is compared with that of current clustering definitions when extended to complete weighted networks.

Keywords

binary networkclustering coefficientcomplete networkdirected networkundirected networkweighted network
Type
Research Article
Information
Network Science , Volume 3 , Issue 2 , June 2015 , pp. 183 - 195
Copyright
Copyright © Cambridge University Press 2015 

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References

Albert, R., & Barabási, A. (2003). Statistical mechanics of complex networks. Reviews of Modern Physics, 74, 47–97.Google Scholar
Barrat, A., Barthélemy, M., Pastor-Satorras, R., & Vespignani, A. (2004). The architecture of complex weighted networks. Proceedings of the National Academy of Sciences, 101 (11), 3747–3752.Google Scholar
Dorogovtsev, S., & Mendes, J. (2003). Evolution of networks: From biological nets to the internet and WWW. Oxford: Oxford University Press.CrossRefGoogle Scholar
Fagiolo, G. (2007). Clustering in complex directed networks. Physical Review E, 76, (026107), 1–8.Google Scholar
Holme, P., Park, S. M., Kim, B. J., & Edling, C. (2007). Korean university life in a network perspective: Dynamics of a large affiliation network. Physica A, 373, 821–830.Google Scholar
Kalna, G., & Higham, D. J. (2006). Clustering coefficients for weighted networks. University of Strathclyde Mathematics Research Report No. 3.Google Scholar
Li, Y., Liu, Y., Li, J., Qin, W., Li, K., et al. (2009). Brain anatomical network and intelligence. PLoS Computational Biology, 5 (5), e1000395. doi: 10.1371/journal.pcbi.1000395.Google Scholar
McAssey, M. P., Bijma, F., Tarigan, B., van Pelt, J., van Ooyen, A., & de Gunst, M. (2013). A morpho-density approach to estimating neural connectivity. PLoS ONE, 9 (1), e86526. doi: 10.1371/journal.pone.0086526.Google Scholar
Newman, M. (2003). The structure and function of complex networks. SIAM Review, 45, 167–256.CrossRefGoogle Scholar
Onnela, J.-P., Saramäki, J., Kertész, J., & Kaski, K. (2005). Intensity and coherence of motifs in weighted complex networks. Physical Review E, 71 (065103), 1–4.Google Scholar
Saramäki, J., Kivelä, M., Onnela, J.-P., Kaski, K., & Kertész, J. (2007). Generalizations of the clustering coefficient to weighted complex networks. Physical Review E, 75 (027105), 1–5.Google Scholar
Szabó, G., Alava, J., & Kertész, J. (2004). Ben-Naim, In, et al. (Eds.), Complex networks. Springer Lecture Notes in Physics volume 650, (pp. 139–162). Berlin: Springer.Google Scholar
Tijms, B. M., Wink, A. M., de Haan, W., van der Flier, W. M., Stam, C. J., Scheltens, P., & Barkhof, F. (2013). Alzheimers disease: Connecting findings from graph theoretical studies of brain networks. Neurobiology of Aging, 34, 2023–2036.Google Scholar
van den Heuvel, M. P., & Fornito, A. (2014). Brain networks in schizophrenia. Neuropsychology Review, 24, 32–48.Google Scholar
Watts, D., & Strogatz, S. (1998). Collective dynamics of small-world networks. Nature, 393, 440–442.CrossRefGoogle ScholarPubMed
Zhang, B., & Horvath, S. (2005). A general framework for weighted gene co-expression network analysis. Statistical Applications in Genetics and Molecular Biology 4, 17.Google Scholar