TY - GEN
T1 - Counting Graphs with a Given Degree Sequence
T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019
AU - Ioushua, Shahar Stein
AU - Shayevitz, Ofer
N1 - Publisher Copyright: © 2019 IEEE.
PY - 2019/7
Y1 - 2019/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85073146014&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2019.8849579
DO - 10.1109/ISIT.2019.8849579
M3 - منشور من مؤتمر
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1492
EP - 1496
BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 7 July 2019 through 12 July 2019
ER -