Premium
The number of graphs and a random graph with a given degree sequence
Author(s) -
Barvinok Alexander,
Hartigan J.A.
Publication year - 2013
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20409
Subject(s) - mathematics , combinatorics , bipartite graph , degree (music) , corollary , discrete mathematics , random regular graph , random graph , sequence (biology) , indifference graph , graph , chordal graph , 1 planar graph , physics , biology , acoustics , genetics
We consider the set of all graphs on n labeled vertices with prescribed degrees D = ( d 1 ,…, d n ). For a wide class of tame degree sequences D we obtain a computationally efficient asymptotic formula approximating the number of graphs within a relative error which approaches 0 as n grows. As a corollary, we prove that the structure of a random graph with a given tame degree sequence D is well described by a certain maximum entropy matrix computed from D . We also establish an asymptotic formula for the number of bipartite graphs with prescribed degrees of vertices, or, equivalently, for the number of 0‐1 matrices with prescribed row and column sums. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom