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Relating Vertex and Global Graph Entropy in Randomly Generated Graphs

by Philip Tee 1,2,*,†,‡, George Parisis 2,‡, Luc Berthouze 2,‡ and Ian Wakeman 2,‡
1
Moogsoft Inc, San Francisco, CA 94111, USA
2
School of Engineering and Informatics, University of Sussex, BN1 9RH Brighton, UK
*
Author to whom correspondence should be addressed.
Current address: Moogsoft Inc, 1265 Battery Street, San Francisco, CA 94111, USA.
These authors contributed equally to this work.
Entropy 2018, 20(7), 481; https://doi.org/10.3390/e20070481
Received: 22 May 2018 / Revised: 14 June 2018 / Accepted: 17 June 2018 / Published: 21 June 2018
(This article belongs to the Special Issue Entropy: From Physics to Information Sciences and Geometry)
Combinatoric measures of entropy capture the complexity of a graph but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of vertex level measures that do not suffer from this pathological computational complexity, but that can be shown to be effective at quantifying graph complexity. In this paper, we consider whether these local measures are fundamentally equivalent to global entropy measures. Specifically, we investigate the existence of a correlation between vertex level and global measures of entropy for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate strong correlation for this subset of graphs and outline how this may arise theoretically. View Full-Text
Keywords: graph entropy; chromatic classes; random graphs graph entropy; chromatic classes; random graphs
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Tee, P.; Parisis, G.; Berthouze, L.; Wakeman, I. Relating Vertex and Global Graph Entropy in Randomly Generated Graphs. Entropy 2018, 20, 481.

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