Achieving exact cluster recovery threshold via semidefinite programming

Bruce Hajek, Yihong Wu, Jiaming Xu

Research output: Contribution to journalArticle


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 independently connected with probability p within clusters and q across clusters. In the asymptotic regime of nand q=b \log n/n for fixed a,b , and n \to \infty , we show that the semidefinite programming relaxation of the maximum likelihood estimator achieves the optimal threshold for exactly recovering the partition from the graph with probability tending to one, resolving a conjecture of Abbe et al. Furthermore, we show that the semidefinite programming relaxation also achieves the optimal recovery threshold in the planted dense subgraph model containing a single cluster of size proportional to $n$.

Original languageEnglish (US)
Article number7440870
Pages (from-to)2788-2797
Number of pages10
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - May 2016



  • Community detection
  • Erdos-Renyi random graph
  • Semidefinite programming
  • Stochastic block model

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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