Passerini, Filippo and Severini, Simone (2008): The von Neumann entropy of networks.

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Abstract
We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study its von Neumann entropy. At the graphtheoretic level, this quantity may be interpreted as a measure of regularity; it tends to be larger in relation to the number of connected components, long paths and nontrivial symmetries. When the set of vertices is asymptotically large, we prove that regular graphs and the complete graph have equal entropy, and specifically it turns out to be maximum. On the other hand, when the number of edges is fixed, graphs with large cliques appear to minimize the entropy.
Item Type:  MPRA Paper 

Original Title:  The von Neumann entropy of networks 
Language:  English 
Keywords:  Networks 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods 
Item ID:  12538 
Depositing User:  Simone Severini 
Date Deposited:  07. Jan 2009 00:54 
Last Modified:  11. Feb 2013 17:09 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/12538 