This is the family of algorithms to which PageRank
The downside of "Katz centrality" compared to PageRank appears to be that if if a big node links to many many nodes, all of those earn a lot of reputation, regardless of how outgoing links there are:
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For a finite undirected graph with at least one edge, eigenvector centrality assigns nonnegative vertex scores proportional to the sum of neighbouring scores: . It uses a nonnegative eigenvector of the adjacency matrix for its largest positive eigenvalue. State the normalization, such as Euclidean norm one. For a three-leaf star graph, hub and leaf scores have ratio .
