期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 111, 期 41, 页码 14722-14727出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1400374111
关键词
community detection; graphons; nonparametric statistics; graph limits; sparse networks
资金
- US Army Research Office under Presidential Early Career Award for Scientists and Engineers [W911NF-09-1-0555]
- Multidisciplinary University Research Initiative Award [W911NF-11-1-0036]
- US Office of Naval Research [N00014-14-1-0819]
- UK Engineering and Physical Sciences Research Council under Mathematical Sciences Leadership Fellowship [EP/I005250/1]
- Established Career Fellowship [EP/K005413/1]
- Developing Leaders Award [EP/L001519/1]
- UK Royal Society under a Wolfson Research Merit Award
- Marie Curie FP7 within 7th European Union Framework Program [PCIG12-GA-2012-334622]
- EPSRC [EP/K005413/1, EP/L001519/1, EP/I005250/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/I005250/1, EP/L001519/1, EP/K005413/1] Funding Source: researchfish
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.
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