Eigenvector-centrality - a node-centrality?

Networks of social relations can be represented by graphs and socio- or adjacency-matrices and their structure can be analyzed using different concepts, one of them called centrality. We will provide a new formalization of a "node-centrality" which leads to some properties a measure of centrality has to satisfy. These properties allow to test given measures, for example measures based on degree. closeness, betweenness or Bonacich's eigenvector-centrality. It turns out that it depends on normalization whether eigenvector-centrality does satisfy the expected properties or not. (C) 2000 Elsevier Science B.V. All rights reserved.