betweenness {sna} | R Documentation |
betweenness
takes a graph stack (dat
) and returns the betweenness centralities of positions within one graph (indicated by nodes
and g
, respectively). Depending on the specified mode, betweenness 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).
betweenness(dat, g=1, nodes=c(1:dim(dat)[2]), gmode="digraph", diag=FALSE, tmaxdev=FALSE, cmode="directed", geodist.precomp=NULL, rescale=FALSE)
dat |
Data array to be analyzed. By assumption, the first dimension of the array indexes the graph, with the next two indexing the actors. Alternately, this can be an n x n matrix (if only one graph is involved). |
g |
Integer indicating the index of the graph for which centralities are to be calculated. By default, g =1. |
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. dmode is set to "digraph" by default. |
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. diag is FALSE by default. |
tmaxdev |
Boolean indicating whether or not the theoretical maximum absolute deviation from the maximum nodal centrality should be returned. By default, tmaxdev ==FALSE . |
cmode |
String indicating the type of betweenness centrality being computed (directed or undirected geodesics). |
geodist.precomp |
A geodist object precomputed for the graph to be analyzed (optional) |
rescale |
If true, centrality scores are rescaled such that they sum to 1. |
The betweenness of a vertex, v, is given by
C_B(v) = sum( g_ivj / g_ij, i,j: i!=j,i!=v,j!=v )
where g_ijk is the number of geodesics from i to k through j. Conceptually, high-betweenness vertices lie on a large number of non-redundant shortest paths between other vertices; they can thus be thought of as ``bridges'' or ``boundary spanners.''
A vector containing the betweenness scores.
Rescale may cause unexpected results if all actors have zero betweenness.
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
Freeman, L.C. (1979). ``Centrality in Social Networks I: Conceptual Clarification.'' Social Networks, 1, 215-239.
g<-rgraph(10) #Draw a random graph with 10 members betweenness(g) #Compute betweenness scores