prestige | R Documentation |
prestige
takes one or more graphs (dat
) and returns the prestige scores of positions (selected by nodes
) within the graphs indicated by g
. Depending on the specified mode, prestige based on any one of a number of different definitions 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).
prestige(dat, g=1, nodes=NULL, gmode="digraph", diag=FALSE,
cmode="indegree", tmaxdev=FALSE, rescale=FALSE, tol=1e-07)
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 |
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. |
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. |
cmode |
one of "indegree", "indegree.rownorm", "indegree.rowcolnorm", "eigenvector", "eigenvector.rownorm", "eigenvector.colnorm", "eigenvector.rowcolnorm", "domain", or "domain.proximity". |
tmaxdev |
boolean indicating whether or not the theoretical maximum absolute deviation from the maximum nodal centrality should be returned. By default, |
rescale |
if true, centrality scores are rescaled such that they sum to 1. |
tol |
Currently ignored |
"Prestige" is the name collectively given to a range of centrality scores which focus on the extent to which one is nominated by others. The definitions supported here are as follows:
indegree: indegree centrality
indegree.rownorm: indegree within the row-normalized graph
indegree.rowcolnorm: indegree within the row-column normalized graph
eigenvector: eigenvector centrality within the transposed graph (i.e., incoming ties recursively determine prestige)
eigenvector.rownorm: eigenvector centrality within the transposed row-normalized graph
eigenvector.colnorm: eigenvector centrality within the transposed column-normalized graph
eigenvector.rowcolnorm: eigenvector centrality within the transposed row/column-normalized graph
domain: indegree within the reachability graph (Lin's unweighted measure)
domain.proximity: Lin's proximity-weighted domain prestige
Note that the centralization of prestige is simply the extent to which one actor has substantially greater prestige than others; the underlying definition is the same.
A vector, matrix, or list containing the prestige scores (depending on the number and size of the input graphs).
Making adjacency matrices doubly stochastic (row-column normalization) is not guaranteed to work. In general, be wary of attempting to try normalizations on graphs with degenerate rows and columns.
Carter T. Butts buttsc@uci.edu
Lin, N. (1976). Foundations of Social Research. New York: McGraw Hill.
Wasserman, S., and Faust, K. (1994). Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press.
centralization
g<-rgraph(10) #Draw a random graph with 10 members
prestige(g,cmode="domain") #Compute domain prestige scores
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