Exact Recovery in Community Detection with Continuous-Valued Side Information

Abstract

The community detection problem, as a special case of inference on graphs, has received much attention lately. However, in the presence of continuous-valued side information, the behavior of a sharp threshold for exact recovery has remained open, and is addressed in this letter. The new proof presented herein has the further advantage of closing the gap between necessary and sufficient conditions for exact recovery threshold that has existed in community detection under finite-alphabet side information.