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I have a graph and don't know how nodes in it are connected to each other.

  • I know the number of nodes in the graph.
  • I know the degree of each node in the graph.
  • I know that given any node $A$ that any other node $B$ is $n$-connected (where $n$ may vary per $B$) to a sub-graph containing $A$. So if I trim $n$ specific edges edges from $B$, then $B$ won't be connected to the sub-graph containing $A$.

The question I want to know is given this information, if it's possible with high probability to learn the entire graph topology.

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    $\begingroup$ The word random has a very specific meaning in mathematics, which is different than its usual English meaning. Similarly, topology is a specific mathematical area, though I can imagine it being used for the “structure” of a graph rather than any topological properties. $\endgroup$ Oct 27, 2021 at 20:45
  • $\begingroup$ One keyword sometimes used for learning a graph is graph reconstruction. $\endgroup$ Oct 28, 2021 at 5:43
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    $\begingroup$ You want to reconstruct the graph "with high probability" — what is the probability over? Everything in your question is deterministic. Perhaps the original graph was chosen according to a specific distribution? $\endgroup$ Oct 31, 2021 at 8:31
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    $\begingroup$ What do you mean when you say that $B$ is $n$-connected to a subgraph containing $A$? When is a node $n$-connected to a graph? $\endgroup$ Oct 31, 2021 at 8:32
  • $\begingroup$ Maybe that's the wrong terminology. But there are n cuts before B and A are disjoint graphs $\endgroup$ Nov 1, 2021 at 13:35

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