Alpha Centrality

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_i the alpha centrality is defined as follows: where e_j is the external importance given to node J, and α is a parameter.

• igraph
  http://igraph.org

• 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]