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Degree-based network models

Olhede, SC; Wolfe, PJ; Degree-based network models.

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Abstract

We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized networks is governed by properties of their degree sequences. We provide exact results and large-sample approximations for power-law networks and other more general forms. This enables us to quantify sampling variability both within and across network populations, and to characterize the limiting extremes of variation achievable through such models. Our results highlight that variation explained through expected degree structure need not be attributed to more complicated generative mechanisms.

Type: Article
Title: Degree-based network models
Additional information: 31 pages, 3 figures, submitted for publication
Keywords: math.ST, math.ST, cs.SI, math.CO, stat.ME, stat.TH, 05C80 (Primary) 62G05, 60B20 (Secondary)
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: http://discovery.ucl.ac.uk/id/eprint/1388625
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