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ENTROPY OF SOME MODELS OF SPARSE RANDOM GRAPHS WITH VERTEX-NAMES

Published online by Cambridge University Press:  31 January 2014

David J. Aldous  and
Nathan Ross
David J. Aldous
Affiliation:
Department of Statistics, 367 Evans Hall no. 3860, U.C. Berkeley, CA 94720 E-mail: [email protected]; www.stat.berkeley.edu/users/aldous
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Abstract

Consider the setting of sparse graphs on N vertices, where the vertices have distinct “names”, which are strings of length O(log N) from a fixed finite alphabet. For many natural probability models, the entropy grows as c N log N for some model-dependent rate constant c. The mathematical content of this paper is the (often easy) calculation of c for a variety of models, in particular for various standard random graph models adapted to this setting. Our broader purpose is to publicize this particular setting as a natural setting for future theoretical study of data compression for graphs, and (more speculatively) for discussion of unorganized versus organized complexity.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 2 , April 2014 , pp. 145 - 168
Copyright
Copyright © Cambridge University Press 2014 

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