Description Usage Arguments Details Value WARNING Author(s) References Examples
eigen_centrality
takes a graph (graph
) and returns the
eigenvector centralities of positions v
within it
1 2  eigen_centrality(graph, directed = FALSE, scale = TRUE,
weights = NULL, options = arpack_defaults)

graph 
Graph to be analyzed. 
directed 
Logical scalar, whether to consider direction of the edges in directed graphs. It is ignored for undirected graphs. 
scale 
Logical scalar, whether to scale the result to have a maximum score of one. If no scaling is used then the result vector has unit length in the Euclidean norm. 
weights 
A numerical vector or 
options 
A named list, to override some ARPACK options. See

Eigenvector centrality scores correspond to the values of the first eigenvector of the graph adjacency matrix; these scores may, in turn, be interpreted as arising from a reciprocal process in which the centrality of each actor is proportional to the sum of the centralities of those actors to whom he or she is connected. In general, vertices with high eigenvector centralities are those which are connected to many other vertices which are, in turn, connected to many others (and so on). (The perceptive may realize that this implies that the largest values will be obtained by individuals in large cliques (or highdensity substructures). This is also intelligible from an algebraic point of view, with the first eigenvector being closely related to the best rank1 approximation of the adjacency matrix (a relationship which is easy to see in the special case of a diagonalizable symmetric real matrix via the $S Λ S^{1}$ decomposition).)
From igraph version 0.5 this function uses ARPACK for the underlying
computation, see arpack
for more about ARPACK in igraph.
A named list with components:
vector 
A vector containing the centrality scores. 
value 
The eigenvalue corresponding to the calculated eigenvector, i.e. the centrality scores. 
options 
A named
list, information about the underlying ARPACK computation. See

eigen_centrality
will not symmetrize your data
before extracting eigenvectors; don't send this routine asymmetric matrices
unless you really mean to do so.
Gabor Csardi [email protected] and Carter T. Butts (http://www.faculty.uci.edu/profile.cfm?faculty_id=5057) for the manual page.
Bonacich, P. (1987). Power and Centrality: A Family of Measures. American Journal of Sociology, 92, 11701182.
1 2 3 4  #Generate some test data
g < make_ring(10, directed=FALSE)
#Compute eigenvector centrality scores
eigen_centrality(g)

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