betweenness {sna} | R Documentation |
betweenness
takes one or more graphs (dat
) and returns the betweenness centralities of positions (selected by nodes
) within the graphs indicated by g
. 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=NULL, gmode="digraph", diag=FALSE, tmaxdev=FALSE, cmode="directed", geodist.precomp=NULL, rescale=FALSE)
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, g =1. |
nodes |
vector 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, matrix, or list containing the betweenness scores (depending on the number and size of the input graphs).
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