Kleinberg's centrality scores.
Kleinberg's hub and authority scores.
authority.score (graph, scale = TRUE, weights=NULL, options = igraph.arpack.default) hub.score (graph, scale = TRUE, weights=NULL, options = igraph.arpack.default)
- The input graph.
- 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.
- Optional positive weight vector for calculating
weighted scores. If the graph has a
weightedge attribute, then this is used by default.
- A named list, to override some ARPACK options. See
The authority scores of the vertices are defined as the principal eigenvector of $A^T A$, where $A$ is the adjacency matrix of the graph.
The hub scores of the vertices are defined as the principal eigenvector of $A A^T$, where $A$ is the adjacency matrix of the graph.
Obviously, for undirected matrices the adjacency matrix is symmetric and the two scores are the same.
- 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
optionsmember returned by
arpack, see that for documentation.
Hub and authority score
J. Kleinberg. Authoritative sources in a hyperlinked environment. Proc. 9th ACM-SIAM Symposium on Discrete Algorithms, 1998. Extended version in Journal of the ACM 46(1999). Also appears as IBM Research Report RJ 10076, May 1997.
## An in-star g <- graph.star(10) hub.score(g)$vector authority.score(g)$vector ## A ring g2 <- graph.ring(10) hub.score(g2)$vector authority.score(g2)$vector