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Network histograms and universality of blockmodel approximation

Olhede, SC; Wolfe, PJ; (2014) Network histograms and universality of blockmodel approximation. Proceedings of the National Academy of Sciences of the United States of America (PNAS) , 111 (41) pp. 14722-14727. 10.1073/pnas.1400374111. Green open access

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Abstract

In this paper we introduce the network histogram, a statistical summary of network interactions to be used as a tool for exploratory data analysis. A network histogram is obtained by fitting a stochastic blockmodel to a single observation of a network dataset. Blocks of edges play the role of histogram bins and community sizes that of histogram bandwidths or bin sizes. Just as standard histograms allow for varying bandwidths, different blockmodel estimates can all be considered valid representations of an underlying probability model, subject to bandwidth constraints. Here we provide methods for automatic bandwidth selection, by which the network histogram approximates the generating mechanism that gives rise to exchangeable random graphs. This makes the blockmodel a universal network representation for unlabeled graphs. With this insight, we discuss the interpretation of network communities in light of the fact that many different community assignments can all give an equally valid representation of such a network. To demonstrate the fidelity-versus-interpretability tradeoff inherent in considering different numbers and sizes of communities, we analyze two publicly available networks—political weblogs and student friendships—and discuss how to interpret the network histogram when additional information related to node and edge labeling is present.

Type: Article
Title: Network histograms and universality of blockmodel approximation
Open access status: An open access version is available from UCL Discovery
DOI: 10.1073/pnas.1400374111
Publisher version: http://dx.doi.org/10.1073/pnas.1400374111
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Community Detection, Graphons, Nonparametric Statistics, Graph Limits, Sparse Networks, Stochastic Blockmodels, Models
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/1427429
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