Information inequalities and Generalized Graph Entropies

Details Information inequalities and Generalized Graph Entropies Information inequalities and Generalized Graph Entropies

2012-02-25

arxiv.org/abs/1202.5685v1

Computer Science

Information Theory

A preliminary version. To be submitted to a journal

Scientific paper

In this article, we discuss the problem of establishing relations between information measures assessed for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the R\'{e}nyi entropy have been considered for this study. Our main results involve establishing formal relationship, in the form of implicit inequalities, between these two kinds of measures when defined for graphs. Further, we also state and prove inequalities connecting the classical partition-based graph entropies and the functional-based entropy measures. In addition, several explicit inequalities are derived for special classes of graphs.

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