Contextual Stochastic Block Model: Sharp Thresholds and Contiguity
This solves a theoretical problem in network analysis for researchers in statistics and machine learning, providing rigorous foundations for community detection with node covariates.
The paper establishes the sharp threshold for community detection in the contextual stochastic block model, confirming a previous conjecture and characterizing the detection and weak recovery limits, specifically when the average degree exceeds one.
We study community detection in the contextual stochastic block model arXiv:1807.09596 [cs.SI], arXiv:1607.02675 [stat.ME]. In arXiv:1807.09596 [cs.SI], the second author studied this problem in the setting of sparse graphs with high-dimensional node-covariates. Using the non-rigorous cavity method from statistical physics, they conjectured the sharp limits for community detection in this setting. Further, the information theoretic threshold was verified, assuming that the average degree of the observed graph is large. It is expected that the conjecture holds as soon as the average degree exceeds one, so that the graph has a giant component. We establish this conjecture, and characterize the sharp threshold for detection and weak recovery.