# Reference request: Network/graph topology inference

I am a mathematician looking for a survey/book on methods for inference of graph/network topology (structure). Specifically, the kind of problem I am looking to study is as follows:

Given a graph $$G$$ consider an unknown function $$f$$ such that $$f(G)=y$$ (for a real number $$y$$). Assume we have a collection of graphs ($$G_1, G_2, \dots, G_n$$) for which the values $$f(G_k)=y_k$$ are known. Given a proposed value $$y_*$$:

• How can one reconstruct a graph $$\hat{G}_*$$ such that $$f(\hat{G}_*)\approx y_*$$?
• How about confidence intervals or high-density regions in some space of graphs?

What I am not interested in is:

• A book such as Durrett's Random Graph Dynamics which presents specific probabilistic models of graph generation but no inference.
• Kolaczyk's Statistical Analysis of Network Data which focuses on inferring part of a network's topological descriptors but not the whole network.