Linear Programming and Community Detection

The problem of community detection with two equal-sized communities is closely related to the minimum graph bisection over certain random models. In stochastic block model distribution networks structure, a well-known semidefinite programming (SDP) relaxation recovers underlying whenever possible. Motivated by their superior scalability, we study theoretical performance linear (LP) relaxations for same We show that, unlike SDP that undergoes phase transition in logarithmic average degree regime, LP fails recovering planted high probability this regime. instead exhibits from recovery nonrecovery Finally, present conditions graphs strictly between and logarithmic. Funding: A. Del Pia partially funded Office Naval Research (ONR) [Grant N00014-19-1-2322]. D. Kunisky supported ONR N00014-20-1-2335], Simons Investigator Award Daniel Spielman, National Science Foundation [Grants DMS-1712730 DMS-1719545].