alpha_centrality {igraph} | R Documentation |
Find Bonacich alpha centrality scores of network positions
Description
alpha_centrality()
calculates the alpha centrality of some (or all)
vertices in a graph.
Usage
alpha_centrality(
graph,
nodes = V(graph),
alpha = 1,
loops = FALSE,
exo = 1,
weights = NULL,
tol = 1e-07,
sparse = TRUE
)
Arguments
graph |
The input graph, can be directed or undirected. In undirected graphs, edges are treated as if they were reciprocal directed ones. |
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 near-singularities during matrix inversion, see
|
sparse |
Logical scalar, whether to use sparse matrices for the calculation. The ‘Matrix’ package is required for sparse matrix support |
Details
The alpha centrality measure can be considered as a generalization of eigenvector centrality 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:
where is the (not necessarily symmetric) adjacency matrix of the
graph,
is the vector of exogenous sources of status of the
vertices and
is the relative importance of the
endogenous versus exogenous factors.
Value
A numeric vector contaning the centrality scores for the selected vertices.
Warning
Singular adjacency matrices cause problems for this algorithm, the routine may fail is certain cases.
Author(s)
Gabor Csardi csardi.gabor@gmail.com
References
Bonacich, P. and Lloyd, P. (2001). “Eigenvector-like measures of centrality for asymmetric relations” Social Networks, 23, 191-201.
See Also
eigen_centrality()
and power_centrality()
Centrality measures
betweenness()
,
closeness()
,
diversity()
,
eigen_centrality()
,
harmonic_centrality()
,
hub_score()
,
page_rank()
,
power_centrality()
,
spectrum()
,
strength()
,
subgraph_centrality()
Examples
# The examples from Bonacich's paper
g.1 <- make_graph(c(1, 3, 2, 3, 3, 4, 4, 5))
g.2 <- make_graph(c(2, 1, 3, 1, 4, 1, 5, 1))
g.3 <- make_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)