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Random multigraphs and aggregated triads with fixed degrees

Published online by Cambridge University Press:  28 December 2017

OVE FRANK
Affiliation:
Department of Statistics, Stockholm University, Sweden (e-mail: ove.frank@stat.su.se)
TERMEH SHAFIE
Affiliation:
Department of Computer & Information Science, University of Konstanz, Germany (e-mail: termeh.shafie@uni-konstanz.de)

Abstract

Random multigraphs with fixed degrees are obtained by the configuration model or by so called random stub matching. New combinatorial results are given for the global probability distribution of edge multiplicities and its marginal local distributions of loops and edges. The number of multigraphs on triads is determined for arbitrary degrees, and aggregated triads are shown to be useful for analyzing regular and almost regular multigraphs. Relationships between entropy and complexity are given and numerically illustrated for multigraphs with different number of vertices and specified average and variance for the degrees.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2017 

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