  Centrality is an important notion in complex networks; it could be used to
characterize how influential a node or an edge is in the network. It plays an
important role in several other network analysis tools including community
detection. Even though there are a small number of axiomatic frameworks
associated with this notion, the existing formalizations are not generic in
nature. In this paper we propose a generic axiomatic framework to capture all
the intrinsic properties of a centrality measure (a.k.a. centrality index). We
analyze popular centrality measures along with other novel measures of
centrality using this framework. We observed that none of the centrality
measures considered satisfies all the axioms.

Social and Information Networks;Physics and Society