Relationships Between Characteristic Path Length, Efficiency, Clustering Coefficients, and Graph Density
Abstract
The graph theoretic properties of the clustering coefficient, characteristic (or average) path length, global and local efficiency, provide valuable information regarding the structure of a graph. These four properties have applications to biological and social networks and have dominated much of the the literature in these fields. While much work has done in applied settings, there has yet to be a mathematical comparison of these metrics from a theoretical standpoint. Motivated by networks appearing in neuroscience, we show in this paper that these properties can be linked together using a single property - graph density.
Cite
@article{arxiv.1702.02621,
title = {Relationships Between Characteristic Path Length, Efficiency, Clustering Coefficients, and Graph Density},
author = {Alexander Strang and Oliver Haynes and Nathan D. Cahill and Darren A. Narayan},
journal= {arXiv preprint arXiv:1702.02621},
year = {2017}
}
Comments
Figure 1 seems to have been dropped during formatting. It can be found at https://ourarchive.otago.ac.nz/handle/10523/4864 Figure 5.8