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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.
kjetil b halvorsen
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Rodrigo Zepeda
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  • A similar reference request exists at [math.stackexchange.com](https://math.stackexchange.com/q/27480/254158) – sboysel Oct 04 '19 at 04:57
  • @sboysel The request at [math.stackexchange.com](https://math.stackexchange.com/questions/27480/what-are-good-books-to-learn-graph-theory) is looking for books on graph theory not for _statistical inference_ on graphs. – Rodrigo Zepeda Oct 04 '19 at 17:41
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    Since $f$ is unknown, I think the first step would be to estimate $f$ before trying to solve the inverse problem $G = f^{-1}(y)$. – 900edges Mar 25 '21 at 14:36
  • Sounds like a great first step. Do you have any references? I'm still looking (two years into this) – Rodrigo Zepeda Mar 25 '21 at 22:15

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