An Extended Family of Measures for Directed Networks

Centrality indices such as beta-centrality, Katz status, and Hubbell's
index are commonly generalized to directed networks by relating the
in-centrality of nodes to the in-centrality of their in-neighbors and
equivalently so for out-centrality. This paper proposes an extension
of Bonacich's beta-centrality and related measures for directed networks
where the in-centrality of a node depends on the out-centrality of their
in-neighbors and their out-centrality on the in-centrality of their out-
neighbors. The so dened indices extend hubs and authorities in the
same way as beta-centrality generalizes eigenvector centrality. Several
technical results are presented including the extension of the range of
permissible parameters to negative values, similar to traditional -
centrality.