Kleinberg's hub and authority scores.

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.

The hub scores of the vertices are defined as the principal eigenvector of A*t(A), 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.

[CSARDI, G. 2006]

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# Kleinberg's Centrality

#### Definition

**See HITS - Hypertext Induced Topic Selection**

Kleinberg's hub and authority scores.

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.

The hub scores of the vertices are defined as the principal eigenvector of A*t(A), 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.

[CSARDI, G. 2006]

#### Requirements

Require connected and loop free network.

#### Software

#### References

- CSARDI, G. & NEPUSZ, T. 2006. The igraph software package for complex network research. InterJournal, Complex Systems, 1695. [http://igraph.org]
- KLEINBERG, J. M. 1999. Authoritative sources in a hyperlinked environment. Journal of the ACM (JACM), 46, 604-632.