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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 (CC BY 3.0).
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Mowshowitz, A.; Dehmer, M. Entropy and the Complexity of Graphs Revisited. Entropy 2012, 14, 559-570.

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