Estimation and Recovery of a Planted Dense Subgraph from a Single Network Cascade

We study the inference of a planted dense component in a sparse random graph from a single spreading process. The graph has an Erdős-Rényi background with edge probability $p_n$ and contains a planted dense component of size $n^α$, with $α> 1/2$, whose internal edge density $ξ>0$ is constant. The ed