closeness {sna} | R Documentation |
closeness
takes a graph stack (dat
) and returns the closeness centralities of positions within one graph (indicated by nodes
and g
, respectively). Depending on the specified mode, closeness 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).
closeness(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. gmode 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 closeness centrality being computed (distances on 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 closeness of a vertex v is defined as
C_C(v) = (|V(G)|-1)/sum( d(v,i), i in V(G), i!=v )
where d(i,j) is the geodesic distance between i and j (where defined). Closeness is ill-defined on disconnected graphs; in such cases, this routine substitutes Inf
. It should be understood that this modification is not canonical (though it is common), but can be avoided by not attempting to measure closeness on disconnected graphs in the first place! Intuitively, closeness provides an index of the extent to which a given vertex has short paths to all other vertices in the graph; this is one reasonable measure of the extent to which a vertex is in the ``middle'' of a given structure.
A vector containing the closeness scores.
Judicious use of geodist.precomp
can save a great deal of time when computing multiple path-based indices on the same network. Before sna
version 0.50, closeness
substituted one plus the maximum possible path length for disconnected vertex pairs.
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 closeness(g) #Compute closeness scores