Institute for Bioinformatics and Translational Research, UMIT, Hall in Tyrol, Austria.
PLoS One. 2012;7(2):e31395. doi: 10.1371/journal.pone.0031395. Epub 2012 Feb 15.
In this article, we tackle a challenging problem in quantitative graph theory. We establish relations between graph entropy measures representing the structural information content of networks. In particular, we prove formal relations between quantitative network measures based on Shannon's entropy to study the relatedness of those measures. In order to establish such information inequalities for graphs, we focus on graph entropy measures based on information functionals. To prove such relations, we use known graph classes whose instances have been proven useful in various scientific areas. Our results extend the foregoing work on information inequalities for graphs.
在本文中，我们解决了定量图论中的一个具有挑战性的问题。我们建立了表示网络结构信息含量的图熵测度之间的关系。特别是，我们证明了基于香农熵的定量网络测度之间的形式关系，以研究这些测度的相关性。为了为图建立这样的信息不等式，我们专注于基于信息泛函的图熵测度。为了证明这些关系，我们使用了已知的图类，其实例已被证明在各个科学领域都很有用。我们的结果扩展了前面关于图的信息不等式的工作。
