Suppose i have a graph $G$ of $n$ nodes. For each node someone has given us a recipe $R$ how to replace the node with a graph. So for node $i$, i have $m_i$ choices of graphs to replace it with. Thus, it is simple to see that given $G$, i can obtain $\prod\limits_{i=1}^n m_i$ graphs because of the recipe $R$ already given. For huge possibilities of graphs that can be obtained from $G$ using $R$, exhaustive enumeration is a poor choice due to computational infeasibility.
To avoid doing exhaustive enumeration because computers cannot run for days, we need to do selective enumeration of those graphs. One idea i could think was that we define biases based on user/operator input. Thus some graphs are more relevant/important than others. Using this as a guiding heuristic we can do some kind of pruning to avoid enumerating all possible graphs.
I have done a lot of hand-waving without any concrete stuff. That is why i posed this question. My question is could someone show some work where this is actually done in a concrete computational way rather than hand-waving, or suggest concrete computational steps to take in this direction?
EDIT:
Suppose we have a directed acyclic graphs with weighted edges. And cost of the graph is a non-linear function of the edge weights. We want to see if changing the graph using $R$ leads to graphs with costs less than some threshold range. We want to avoid doing exhaustive enumeration and do some smart algo method. What previous work has been done in this direction? What keywords to search in google scholar to find such algo methods?