Section: New Results
An Impossibility Result for Reconstruction in a Degree-Corrected Planted-Partition Model
In a paper currently in preparation  , we consider a degree-corrected planted-partition model: a random graph on nodes with two equal-sized clusters. The model parameters are two constants and an i.i.d. sequence , with finite second moment . Vertices and are joined by an edge with probability whenever they are in the same class and with probability otherwise. We prove that the underlying community structure cannot be accurately recovered from observations of the graph when .