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To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model.
Stochastic blockmodels: First steps
P. W. Holland, K. B. Laskey, and S. Leinhardt · 1983
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The solution of some random np-hard problems in polynomial expected time
M. E. Dyer and A. M. Frieze · 1989
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On a continuum percolation model
M. D. Penrose · 1991
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Random graphs
B. Bollobás · 1998
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Critical power for asymptotic connectivity
P. Gupta and P. R. Kumar · 1998
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On the minimum node degree and connectivity of a wireless multihop network
C. Bettstetter · 2002
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Community structure in social and biological networks
M. Girvan and M. E. Newman · 2002
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Random geometric graphs
M. Penrose · 2003
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Correlation clustering
N. Bansal, A. Blum, and S. Chawla · 2004
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The political blogosphere and the 2004 us election: divided they blog
L. A. Adamic and N. Glance · 2005
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Monotone properties of random geometric graphs have sharp thresholds
A. Goel, S. Rai, and B. Krishnamachari · 2005
Cited alongside, same era.
On the cover time and mixing time of random geometric graphs
C. Avin and G. Ercal · 2007
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The dynamics of viral marketing
J. Leskovec, L. A. Adamic, and B. A. Huberman · 2007
Cited alongside, same era.
Statistical properties of community structure in large social and information networks
J. Leskovec, K. J. Lang, A. Dasgupta, and M. W. Mahoney · 2008
Cited alongside, same era.
Stochastic geometry and random graphs for the analysis and design of wireless networks
M. Haenggi, J. G. Andrews, F. Baccelli, O. Dousse, and M. Franceschetti · 2009
Cited alongside, same era.
Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
Recovering communities in the general stochastic block model without knowing the parameters
E. Abbe and C. Sandon · 2015
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P. Chin, A. Rao, and V. Vu · 2015
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Computational lower bounds for community detection on random graphs
B. E. Hajek, Y. Wu, and J. Xu · 2015
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Consistency of spectral clustering in stochastic block models
J. Lei, A. Rinaldo, et al · 2015
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Consistency thresholds for the planted bisection model
E. Mossel, J. Neeman, and A. Sly · 2015
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Defining and evaluating network communities based on ground-truth
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A. Decelle, F. Krzakala, C. Moore, and L. Zdeborová · 2011
Cited alongside, same era.
High-dimensional random geometric graphs and their clique number
L. Devroye, A. György, G. Lugosi, F. Udina, et al · 2011
Cited alongside, same era.
Spectral clustering and the high-dimensional stochastic blockmodel
K. Rohe, S. Chatterjee, B. Yu, et al · 2011
Cited alongside, same era.
Community detection in general stochastic block models: Fundamental limits and efficient algorithms for recovery
E. Abbe and C. Sandon · 2015
Cited alongside, same era.
Concentration inequalities
S. Boucheron, G. Lugosi, and O. Bousquet
Cited in the paper.
J. Yang and J. Leskovec · 2015
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Exact recovery in the stochastic block model
E. Abbe, A. S. Bandeira, and G. Hall · 2016
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Testing for high-dimensional geometry in random graphs
S. Bubeck, J. Ding, R. Eldan, and M. Z. Rácz · 2016
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Achieving exact cluster recovery threshold via semidefinite programming
B. Hajek, Y. Wu, and J. Xu · 2016
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