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Degree-Based Network Models

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We present an analysis of degree-based network models: ones in which the structure of realized networks is governed by properties of degree sequences. Many such models are understood only asymptotically; for finitely many nodes, they yield neither closed-form statistical likelihoods nor precise forward generating mechanisms. In contrast, we provide exact statistical results, limit theorems, and large-sample approximations that govern the behavior of networks based on weights whose pairwise products parameterize independent Bernoulli trials. This yields a clear understanding of sampling variability both within and across network populations, and a characterization of limiting extremes of variation achievable through such models. These results highlight that variation explained through expected degree structure need not be attributed to more complicated generative mechanisms.

Biographical Details:

Patrick J. Wolfe is Professor of Statistics and Honorary Professor of Computer Science at University College London, where he is a member of the Department’s Senior Management Team and a Royal Society Research Fellow. From 2001-2004 he held a Fellowship and College Lectureship in Engineering and Computer Science at Cambridge University, where he completed his PhD in 2003. Prior to joining UCL he was Assistant (2004-2008) and Associate (2008-2011) Professor at Harvard University. He serves on the Research Section Committee of the Royal Statistical Society, and on the editorial boards of Applied and Computational Harmonic Analysis and the IEEE ’s Signal Processing Magazine.

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