Abstract
In this paper, we explore the relationship between two metrics that appear in the literature of social networks, local efficiency and the clustering coefficients. Next, we investigate these properties for a selection of real-world networks involving fMRI data from athletes and show for non-sparse graphs the relationship between the two properties is very close to linear.
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Acknowledgments
The authors are grateful to anonymous referees for many comments that improved the presentation of this paper. In particular we are grateful that references Borgatti (2006), Davis (1967), Ek et al. (2013) and Freeman (1979) were brought to our attention. Research was supported through a National Science Foundation Research Experiences for Undergraduates Grant, Award Number: 1062128.
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Appendix
Appendix
A prototype implementation for computing the various graph properties described in this paper is available for download at MATLAB Central (http://www.mathworks.com/matlabcentral/) under File ID #46084.
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Ek, B., VerSchneider, C., Cahill, N.D. et al. A comprehensive comparison of graph theory metrics for social networks. Soc. Netw. Anal. Min. 5, 37 (2015). https://doi.org/10.1007/s13278-015-0272-2
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DOI: https://doi.org/10.1007/s13278-015-0272-2