Construct a graph $H$ with $3n$ nodes in this way:
- Create three $G(n, p)$ graphs on a line, each with $p{n \choose 2}$ many edges within each cluster.
- For any node-pair in the neighboring clustering, add edges between them with probability $q$. Hence we'd end up with $qn^2$ many nodes collecting the nodes of the neighboring clusters.
Question: what is the probability that we'd have at least a path connecting the left-most cluster to the right-most cluster, in terms of $p$, $q$, and $n$.
