Abstract
The degree-based network entropy which is inspired by Shannon’s entropy concept becomes the information-theoretic quantity for measuring the structural information of graphs and complex networks. In this paper, we study some properties of the degree-based network entropy. Firstly we develop a refinement of Jensen’s inequality. Next we present the new and more accurate upper bound and lower bound for the degree-based network entropy only using the order, the size, the maximum degree and minimum degree of a network. The bounds have desirable performance to restrict the entropy in different kinds of graphs. Finally, we show an application to structural complexity analysis of a computer network modeled by a connected graph.
Highlights
The entropy of a probability distribution is known as a measure of unpredictability of information content, or a measure of uncertainty of a system
We focus on the degree-based network entropy introduced by Dehmer all the time
We studied the properties for degree-based network entropy NE
Summary
The entropy of a probability distribution is known as a measure of unpredictability of information content, or a measure of uncertainty of a system. Dehmer [16,17,18,19,20] introduced graph entropies based on information functionals which capture structural information and studied their properties. He assigned a probability value to each individual node in a graph or a network. This paper is organized as follows: In Section 2, some notations in graph theory and the degree-based network entropy we are going to study are introduced. A short summary and conclusion are drawn in the last section
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