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Entropy 2012, 14(3), 559-570; doi:10.3390/e14030559
Article

Entropy and the Complexity of Graphs Revisited

1,*  and 2,*
1 Department of Computer Science, The City College of New York (CUNY), 138th Street at ConventAvenue, New York, NY 10031, USA 2 Institute for Bioinformatics and Translational Research, UMIT, Eduard Wallnoefer Zentrum 1, 6060, Hall in Tyrol, Austria
* Authors to whom correspondence should be addressed.
Received: 16 January 2012 / Revised: 5 March 2012 / Accepted: 12 March 2012 / Published: 14 March 2012
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Abstract

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.
Keywords: complex networks; Shannon entropy; graph entropy complex networks; Shannon entropy; graph entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Mowshowitz, A.; Dehmer, M. Entropy and the Complexity of Graphs Revisited. Entropy 2012, 14, 559-570.

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