Edge centrality measures are functions that evaluate the importance of edges in a network. They can be used to assess role backlink for popularity website as well flight virus spreading. Various node centralities have been translated apply edges, including Betweenness, Eigenedge (edge version eigenvector centrality), and PageRank. With this paper, we initiate discussion on axiomatic properties ...

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.

We formulate and prove an axiomatic characterization of conditional information geometry, for both the normalized and the nonnormalized cases. This characterization extends the axiomatic derivation of the Fisher geometry by Čencov and Campbell to the cone of positive conditional models, and as a special case to the manifold of conditional distributions. Due to the close connection between the c...

Axiomatic characterizations of Shannon entropy, Kullback I-divergence, and some generalized information measures are surveyed. Three directions are treated: (A) Characterization of functions of probability distributions suitable as information measures. (B) Characterization of set functions on the subsets of {1, . . . , N} representable by joint entropies of components of an N -dimensional rand...