Entity

Time filter

Source Type


Dehmer M.,Institute for Bioinformatics and Translational Research | Dehmer M.,Vienna University of Technology | Mowshowitz A.,City College of New York
Information Sciences | Year: 2011

This survey seeks to describe methods for measuring the entropy of graphs and to demonstrate the wide applicability of entropy measures. Setting the scene with a review of classical measures for determining the structural information content of graphs, we discuss graph entropy measures which play an important role in a variety of problem areas, including biology, chemistry, and sociology. In addition, we examine relationships between selected entropy measures, illustrating differences quantitatively with concrete examples. © 2010 Elsevier Inc. All rights reserved. Source


Cao S.,Nankai University | Dehmer M.,Institute for Bioinformatics and Translational Research | Shi Y.,Nankai University
Information Sciences | Year: 2014

Many graph invariants have been used for the construction of entropy-based measures to characterize the structure of complex networks. Based on Shannon's entropy, we study graph entropies which are based on vertex degrees by using so-called information functionals. When considering Shannon entropy-based graph measures, there has been very little work to find their extremal values. The main contribution of this paper is to prove some extremal values for the underlying graph entropy of certain families of graphs and to find the connection between the graph entropy and the sum of degree powers. Further, conjectures to determine extremal values of graph entropies are given. © 2014 Elsevier Inc. All rights reserved. Source


Dehmer M.,Institute for Bioinformatics and Translational Research
Symmetry | Year: 2011

The paper puts the emphasis on surveying information-theoretic network measures for analyzing the structure of networks. In order to apply the quantities interdisciplinarily, we also discuss some of their properties such as their structural interpretation and uniqueness. © 2011 by the author. Source


Mowshowitz A.,City College of New York | Dehmer M.,Institute for Bioinformatics and Translational Research
Entropy | Year: 2012

This paper presents a taxonomy and overview of approaches to the measurement of graph and network complexity. The taxonomy distinguishes between deterministic (e.g., Kolmogorov complexity) and probabilistic approaches with a view to placing entropy-based probabilistic measurement in context. Entropy-based measurement is the main focus of the paper. Relationships between the different entropy functions used to measure complexity are examined; and intrinsic (e.g., classical measures) and extrinsic (e.g., Körner entropy) variants of entropy-based models are discussed in some detail. © 2012 by the authors. Source


Dehmer M.,Institute for Bioinformatics and Translational Research | Shi Y.,Nankai University
PLoS ONE | Year: 2014

In this paper, we examine the uniqueness (discrimination power) of a newly proposed graph invariant based on the matrix DMAX defined by Randić et al. In order to do so, we use exhaustively generated graphs instead of special graph classes such as trees only. Using these graph classes allow us to generalize the findings towards complex networks as they usually do not possess any structural constraints. We obtain that the uniqueness of this newly proposed graph invariant is approximately as low as the uniqueness of the Balaban J index on exhaustively generated (general) graphs. Copyright: © 2014 Dehmer, Shi. Source

Discover hidden collaborations