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Relating vertex and global graph entropy in randomly generated graphs
journal contribution
posted on 2023-06-09, 13:54 authored by Philip Tee, George ParisisGeorge Parisis, Luc BerthouzeLuc Berthouze, Ian WakemanIan WakemanCombinatoric 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.
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Publication status
- Published
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- Published version
Journal
EntropyISSN
1099-4300Publisher
MDPIExternal DOI
Issue
7Volume
20Department affiliated with
- Informatics Publications
Research groups affiliated with
- Foundations of Software Systems Publications
- Evolutionary and Adaptive Systems Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2018-06-22First Open Access (FOA) Date
2018-06-22First Compliant Deposit (FCD) Date
2018-06-21Usage metrics
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