Counting Graphs with a Given Degree Sequence: An Information-theoretic Perspective

Shahar Stein Ioushua, Ofer Shayevitz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We revisit the problem of counting the number of directed graphs with a specified degree sequence, which was recently studied and solved by Barvinok using generating functions and convex duality techniques. We describe a systematic information-theoretic approach to this type of problems, based on studying invariant distributions and establishing suitable continuity and concentration properties. Our techniques recover and shed further light on Barvinok's solution, and may be applicable in other similar problems. As a simple example, we also apply our approach to estimating the number of undirected graphs with a given degree sequence. In particular, we show this number is approximately given by the square root of the number of associated directed graphs, whose input and output degree sequences are equal to that of the undirected graph.

Original languageEnglish
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1492-1496
Number of pages5
ISBN (Electronic)9781538692912
DOIs
StatePublished - Jul 2019
Event2019 IEEE International Symposium on Information Theory, ISIT 2019 - La Maison de La Mutualité, Paris, France
Duration: 7 Jul 201912 Jul 2019

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2019-July
ISSN (Print)2157-8095

Conference

Conference2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/TerritoryFrance
CityParis
Period7/07/1912/07/19

Funding

FundersFunder number
Israel Science Foundation1495/18

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