Use this if you are using igraph from R
The authority scores of the vertices are defined as the principal eigenvector of t(A)*A, where A is the adjacency matrix of the graph.
authority_score(graph, scale = TRUE, weights = NULL, options = arpack_defaults)
graph 
The input graph. 
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 
Optional positive weight vector for calculating weighted
scores. If the graph has a 
options 
A named list, to override some ARPACK options. See

For undirected matrices the adjacency matrix is symmetric and the
authority scores are the same as hub scores, see
hub_score
.
A named list with members:
vector 
The authority/hub scores of the vertices. 
value 
The corresponding eigenvalue of the calculated principal eigenvector. 
options 
Some information about the ARPACK computation, it has
the same members as the 
J. Kleinberg. Authoritative sources in a hyperlinked environment. Proc. 9th ACMSIAM Symposium on Discrete Algorithms, 1998. Extended version in Journal of the ACM 46(1999). Also appears as IBM Research Report RJ 10076, May 1997.
hub_score
, eigen_centrality
for
eigenvector centrality, page_rank
for the Page Rank
scores. arpack
for the underlining machinery of the
computation.
## An instar g < make_star(10) hub_score(g)$vector authority_score(g)$vector ## A ring g2 < make_ring(10) hub_score(g2)$vector authority_score(g2)$vector