Use this if you are using igraph from R
See centralize
for a summary of graph centralization.
centr_eigen( graph, directed = FALSE, scale = TRUE, options = arpack_defaults, normalized = TRUE )
graph 
The input graph. 
directed 
logical scalar, whether to use directed shortest paths for calculating eigenvector centrality. 
scale 
Whether to rescale the eigenvector centrality scores, such that the maximum score is one. 
options 
This is passed to 
normalized 
Logical scalar. Whether to normalize the graph level centrality score by dividing by the theoretical maximum. 
A named list with the following components:
vector 
The nodelevel centrality scores. 
value 
The corresponding eigenvalue. 
options 
ARPACK options, see the return value of

centralization 
The graph level centrality index. 
theoretical_max 
The same as above, the theoretical maximum centralization score for a graph with the same number of vertices. 
Other centralization related:
centr_betw_tmax()
,
centr_betw()
,
centr_clo_tmax()
,
centr_clo()
,
centr_degree_tmax()
,
centr_degree()
,
centr_eigen_tmax()
,
centralize()
# A BA graph is quite centralized g < sample_pa(1000, m = 4) centr_degree(g)$centralization centr_clo(g, mode = "all")$centralization centr_betw(g, directed = FALSE)$centralization centr_eigen(g, directed = FALSE)$centralization # The most centralized graph according to eigenvector centrality g0 < make_graph(c(2,1), n = 10, dir = FALSE) g1 < make_star(10, mode = "undirected") centr_eigen(g0)$centralization centr_eigen(g1)$centralization