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Refining the clustering coefficient for analysis of social and neural network data

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Abstract

In this paper we show how a deeper analysis of the clustering coefficient in a network can be used to assess functional connections in the human brain. Our metric of edge clustering centrality considers the frequency at which an edge appears across all local subgraphs that are induced by each vertex and its neighbors. This analysis is tied to a problem from structural graph theory in which we seek the largest subgraph that is a Cartesian product of two complete bipartite graphs \(K_{1,m}\) and \(K_{1,1}\). We investigate this property and compare it to other known edge centrality metrics. Finally, we apply the property of clustering centrality to an analysis of functional MRI data obtained, while healthy participants pantomimed object use or identified objects.

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Acknowledgments

Roger Vargas’s research was supported by a NSF Research Experiences for Undergraduates Grant at the Rochester Institute of Technology #1358583, under the direction of Darren Narayan. Darren Narayan was also supported by NSF Award #1019532. The acquisition and analysis of the MRI data reported herein was supported by NIH Grant NS089609 to Bradford Mahon. Preparation of this manuscript was supported by NIH Grant NSO89069 and NSF Grant 1349042 to Bradford Mahon. Frank Garcea was supported by a University of Rochester Center for Visual Science pre-doctoral training fellowship (NIH training Grant 5T32EY007125-24).

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Authors and Affiliations

  1. Mathematics and Statistics, Williams College, Williamstown, USA

    Roger Vargas

  2. Department of Brain and Cognitive Sciences, University of Rochester, Rochester, USA

    Frank Garcea & Bradford Z. Mahon

  3. Center for Visual Science, University of Rochester, Rochester, USA

    Frank Garcea & Bradford Z. Mahon

  4. Department of Neurosurgery, University of Rochester, Medical Center, Rochester, USA

    Bradford Z. Mahon

  5. School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY, USA

    Darren A. Narayan

  6. Rochester Center for Brain Imaging, University of Rochester, Rochester, USA

    Darren A. Narayan

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  1. Roger Vargas
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  2. Frank Garcea
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  3. Bradford Z. Mahon
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  4. Darren A. Narayan
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Corresponding author

Correspondence to Darren A. Narayan.

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Vargas, R., Garcea, F., Mahon, B.Z. et al. Refining the clustering coefficient for analysis of social and neural network data. Soc. Netw. Anal. Min. 6, 49 (2016). https://doi.org/10.1007/s13278-016-0361-x

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  • DOI: https://doi.org/10.1007/s13278-016-0361-x

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