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# Alpha Centrality

#### Definition

Alpha centrality is an adaptation of eigenvector centrality in directed graph with the addition that nodes are imbued with importance from external sources.

Given a graph with adjacency matrix A

Given a graph with adjacency matrix A

_{i}the alpha centrality is defined as follows: where e_{j}is the external importance given to node J, and α is a parameter.#### Software

#### References

- BONACICH, P. & LLOYD, P. 2001. Eigenvector-like measures of centrality for asymmetric relations. Social Networks, 23, 191-201.
- CSARDI, G. & NEPUSZ, T. 2006. The igraph software package for complex network research. InterJournal, Complex Systems, 1695. [http://igraph.org]