Harary Graph Centrality


Definition


See Eccentricity Centrality

Graph centrality measures the length of the shortest path to reach the node farthest away from the given node.
The Harary graph centrality of a vertex v is equal to:

1/(maxu d(v,u))

where d(v,u) is the geodesic distance from v to u. Vertices with low graph centrality scores are likely to be near the “edge” of a graph, while those with high scores are likely to be near the “middle.” Compare this with closeness, which is based on the reciprocal of the sum of distances to all other vertices (rather than simply the maximum).

Software

References

  • CARTER T. BUTTS (2014). sna: Tools for Social Network Analysis. R package version 2.3-2. http://CRAN.R-project.org/package=sna
  • HAGE, P. & HARARY, F. 1995. Eccentricity and centrality in networks. Social Networks, 17, 57-63. DOI: 10.1016/0378-8733(94)00248-9 Publisher web site Endnote RIS file