A nonparametric view of network models and Newman–Girvan and other modularities

By Peter J. Bickel, Aiyou Chen. Proceedings of the National Academy of Sciences of the United States of America, 2009

887 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b1ce2c495ca94310a41dc432fa4dc7b907a1a2f4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

In Statistical and Nonlinear Physics

Citations in the corpus

FAST COMMUNITY DETECTION BY SCORE (2012, background): “In most part of the paper, the eigenvalues of interest are simple (i.e., algebraic multiplicity 1 [18]).”
Convergence and concentration of empirical measures under Wasserstein distance in unbounded functional spaces (2018, methodology): “Exchangeable random graphs [2, 21, 22] have been an important probabilistic tool in network research [4, 28].”
Community Detection in General Stochastic Block models: Fundamental Limits and Efficient Algorithms for Recovery (2015, background): “Recently, similar phenomena have been identified for the stochastic block model (SBM), one of the most popular network models exhibiting community structures [20], [21], [22], [23], [24], [25].”
Econometrics of Network Formation (2016, methodology): “Estimating such a model directly from the data is infeasible, but a reasonable approach to get at this was developed by Bickel and Chen (2009), where individuals belong to communities and the number of communities grows asymptotically. Setting aside computational complexity issues, we find that a ma”
Scalable Inference of Overlapping Communities (2012, methodology): “Classical methods for community detection assume that each node participates in a single community [4, 5, 6].”
Statistical Inference on Random Dot Product Graphs: a Survey (2017, background): “This work and the work of Bickel and Chen [12] both consider the case of very sparse graphs.”
Graph Clustering with Graph Neural Networks (2020, methodology): “Thus, the SBM has been used to analyze graph clustering algorithms both theoretically (Bickel and Chen, 2009; Abbe and Sandon, 2015) and empirically (Mothe et al.”
A Consistent Adjacency Spectral Embedding for Stochastic Blockmodel Graphs (2011, background): “Bickel and Chen (2009) showed that maximizing the Newman–Girvan modularity (Newman and Girvan 2004) or the likelihood modularity provides consistent estimation of block membership.”
Consistency of community detection in networks under degree-corrected stochastic block models (2011, methodology): “There has been little theoretical analysis of community detection methods until very recently, when a consistency framework for community detection was introduced by Bickel and Chen [5].”
Pseudo-likelihood methods for community detection in large sparse networks (2012, background): “…with an edge-probability matrix of the form e Note that the only additional restriction we are imposing is that P has the same diagonal entries. e This is a slightly diﬀerent parametrization from the more conventional P n = ρ n S [6], where S (and π ) do not depend on n , and λ n = ρ n π T Sπ .”