2005/06/06 by Petter Holme · 2 citations
Physics and Astronomy · #physics.soc-ph
paper · pdf · doi:10.1103/physreve.72.046111
published as Phys. Rev. E 72, 046111 (2005)
arxiv created 2005/06/06 · arxiv updated 2009/12/01
Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy. We measure this coefficient for a number of real-world and model networks and find that different classes of networks have their characteristic values. For example do geographical networks have a strong core-periphery structure, while the core-periphery structure of social networks (despite their positive degree-degree correlations) is rather weak. We proceed to study radial statistics of the core, i.e. properties of the n-neighborhoods of the core vertices for increasing n. We find that almost all networks have unexpectedly many edges within n-neighborhoods at a certain distance from the core suggesting an effective radius for non-trivial network processes.