alpha_centrality  R Documentation 
alpha_centrality
calculates the alpha centrality of some (or all)
vertices in a graph.
alpha_centrality( graph, nodes = V(graph), alpha = 1, loops = FALSE, exo = 1, weights = NULL, tol = 1e07, sparse = TRUE )
graph 
The input graph, can be directed or undirected 
nodes 
Vertex sequence, the vertices for which the alpha centrality values are returned. (For technical reasons they will be calculated for all vertices, anyway.) 
alpha 
Parameter specifying the relative importance of endogenous versus exogenous factors in the determination of centrality. See details below. 
loops 
Whether to eliminate loop edges from the graph before the calculation. 
exo 
The exogenous factors, in most cases this is either a constant – the same factor for every node, or a vector giving the factor for every vertex. Note that too long vectors will be truncated and too short vectors will be replicated to match the number of vertices. 
weights 
A character scalar that gives the name of the edge attribute
to use in the adjacency matrix. If it is 
tol 
Tolerance for nearsingularities during matrix inversion, see

sparse 
Logical scalar, whether to use sparse matrices for the calculation. The ‘Matrix’ package is required for sparse matrix support 
The alpha centrality measure can be considered as a generalization of eigenvector centerality to directed graphs. It was proposed by Bonacich in 2001 (see reference below).
The alpha centrality of the vertices in a graph is defined as the solution of the following matrix equation:
x=alpha t(A)x+e,
where A is the (not necessarily symmetric) adjacency matrix of the graph, e is the vector of exogenous sources of status of the vertices and alpha is the relative importance of the endogenous versus exogenous factors.
A numeric vector contaning the centrality scores for the selected vertices.
Singular adjacency matrices cause problems for this algorithm, the routine may fail is certain cases.
Gabor Csardi csardi.gabor@gmail.com
Bonacich, P. and Lloyd, P. (2001). “Eigenvectorlike measures of centrality for asymmetric relations” Social Networks, 23, 191201.
eigen_centrality
and power_centrality
# The examples from Bonacich's paper g.1 < graph( c(1,3,2,3,3,4,4,5) ) g.2 < graph( c(2,1,3,1,4,1,5,1) ) g.3 < graph( c(1,2,2,3,3,4,4,1,5,1) ) alpha_centrality(g.1) alpha_centrality(g.2) alpha_centrality(g.3,alpha=0.5)
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