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

@article{Aldous2014ENTROPYOS,
  title={ENTROPY OF SOME MODELS OF SPARSE RANDOM GRAPHS WITH VERTEX-NAMES},
  author={David J. Aldous and Nathan Ross},
  journal={Probability in the Engineering and Informational Sciences},
  year={2014},
  volume={28},
  pages={145 - 168}
}
  • D. Aldous, Nathan Ross
  • Published 2 January 2013
  • Computer Science
  • Probability in the Engineering and Informational Sciences
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… 
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