Entropy of Digraphs and Infinite Networks

A. Mowshowitz ()
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A. Mowshowitz: The City College of New York (CUNY), Department of Computer Science

Chapter Chapter 1 in Towards an Information Theory of Complex Networks, 2011, pp 1-16 from Springer

Abstract: Abstract The information content of a graph G is defined in Mowshowitz (Bull Math Biophys 30:175–204, 1968) as the entropy of a finite probability scheme associated with the vertex partition determined by the automorphism group of G. This provides a quantitative measure of the symmetry structure of a graph that has been applied to problems in such diverse fields as chemistry, biology, sociology, and computer science (Mowshowitz and Mitsou, Entropy, orbits and spectra of graphs, Wiley-VCH, 2009). The measure extends naturally to directed graphs (digraphs) and can be defined for infinite graphs as well (Mowshowitz, Bull Math Biophys 30:225–240, 1968).This chapter focuses on the information content of digraphs and infinite graphs. In particular, the information content of digraph products and recursively defined infinite graphs is examined.

Keywords: Digraphs; Entropy; Infinite graphs; Information content; Networks (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-0-8176-4904-3_1

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