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The binary symmetric stochastic block model deals with a random graph of $n$ vertices partitioned into two equal-sized clusters, such that each pair of vertices is connected independently with probability $p$ within clusters and $q$ across clusters.
On random graphs, I
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P. W. Holland, K. B. Laskey, and S. Leinhardt · 1983
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Improved approximation algorithms for MAX k-CUT and MAX BISECTION
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Finding a large hidden clique in a random graph
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Algorithms for graph partitioning on the planted partition model
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