Compute the (Harary) Graph Centrality Scores of Network Positions
graphcent takes one or more graphs (dat) and returns the Harary graph centralities of positions (selected by nodes) within the graphs indicated by g. Depending on the specified mode, graph centrality on directed or undirected geodesics will be returned; this function is compatible with centralization, and will return the theoretical maximum absolute deviation (from maximum) conditional on size (which is used by centralization to normalize the observed centralization score).
graphcent(dat, g=1, nodes=NULL, gmode="digraph", diag=FALSE,
tmaxdev=FALSE, cmode="directed", geodist.precomp=NULL,
rescale=FALSE, ignore.eval)dat |
one or more input graphs. |
g |
integer indicating the index of the graph for which centralities are to be calculated (or a vector thereof). By default, |
nodes |
list indicating which nodes are to be included in the calculation. By default, all nodes are included. |
gmode |
string indicating the type of graph being evaluated. "digraph" indicates that edges should be interpreted as directed; "graph" indicates that edges are undirected. |
diag |
boolean indicating whether or not the diagonal should be treated as valid data. Set this true if and only if the data can contain loops. |
tmaxdev |
boolean indicating whether or not the theoretical maximum absolute deviation from the maximum nodal centrality should be returned. By default, |
cmode |
string indicating the type of graph centrality being computed (directed or undirected geodesics). |
geodist.precomp |
a |
rescale |
if true, centrality scores are rescaled such that they sum to 1. |
ignore.eval |
logical; should edge values be ignored when calculating geodesics? |
The Harary graph centrality of a vertex v is equal to 1/(max_u 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).
A vector, matrix, or list containing the centrality scores (depending on the number and size of the input graphs).
Judicious use of geodist.precomp can save a great deal of time when computing multiple path-based indices on the same network.
Carter T. Butts buttsc@uci.edu
Hage, P. and Harary, F. (1995). “Eccentricity and Centrality in Networks.” Social Networks, 17:57-63.
g<-rgraph(10) #Draw a random graph with 10 members graphcent(g) #Compute centrality scores
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