Related papers: Information inequalities and Generalized Graph Ent…
The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph \cite{DM1,M}. After Shannon introduced the definition of entropy to information and communication, many generalizations of the entropy…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
We introduce the (private) entropy of a directed graph (in a new network coding sense) as well as a number of related concepts. We show that the entropy of a directed graph is identical to its guessing number and can be bounded from below…
Entropic measures of complexity are able to quantify the information encoded in complex network structures. Several entropic measures have been proposed in this respect. Here we study the relation between the Shannon entropy and the Von…
In estimating the complexity of objects, in particular of graphs, it is common practice to rely on graph- and information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these…
The R{\'e}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{\'e}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
The von Neumann graph entropy is a measure of graph complexity based on the Laplacian spectrum. It has recently found applications in various learning tasks driven by networked data. However, it is computational demanding and hard to…
The entropy of a graph was first introduced by Rashevsky \cite{Rashevsky} and Trucco \cite{Trucco} to interpret as the structural information content of the graph and serve as a complexity measure. In this paper, we first state a number of…
Shannon entropy is the most crucial foundation of Information Theory, which has been proven to be effective in many fields such as communications. Renyi entropy and Chernoff information are other two popular measures of information with…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
In this paper have written the results of the information analysis of structures. The obtained information estimation (IE) are based on an entropy measure of C. Shannon. Obtained IE is univalent both for the non-isomorphic and for the…
Quantifying the complexity of large graphs requires measures that extend beyond predefined structural features and scale efficiently with graph size. This work adopts a generative perspective, modeling large networks as exchangeable graphs…
Existing polarization theories have mostly been concerned with Shannon's information measures, such as Shannon entropy and mutual information, and some related measures such as the Bhattacharyya parameter. In this work, we extend…
Algorithmic entropy and Shannon entropy are two conceptually different information measures, as the former is based on size of programs and the later in probability distributions. However, it is known that, for any recursive probability…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
In the past over two decades, very fruitful results have been obtained in information theory in the study of the Shannon entropy. This study has led to the discovery of a new class of constraints on the Shannon entropy called…
A new conceptual foundation for the notion of "information" is proposed, based on the concept of a "distinction graph": a graph in which two nodes are connected iff they cannot be distinguished by a particular observer. The "graphtropy" of…
In this work, we investigate the reliability of information-theoretic measures based on the electron-density and shape-function, specifically Shannon and R\'enyi entropies, as descriptors of electronic correlation. By establishing a…
We propose R\'enyi information generating function and discuss its properties. A connection between the R\'enyi information generating function and the diversity index is proposed for discrete type random variables. The relation between the…