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I have a directed graph with hierarchical structure, multiple nodes and edge types. One node can have different in- and outgoing connections. There would also be more details to some of the nodes – e.g. subtypes but I am not sure how I can incorporate this information in the analysis.

The graph data is originally stored in XML. For now, I parsed it and stored it in a json file. So I have the file with all different nodes and edges and how they are connected.

I want to identify structural similarities and dissimilarities while consider hierarchy of the graphs.

What methods exist to compare directed multi-edge hierarchical graphs in terms of structure?

My Goal is to be able to make concrete Statements: E.g.: Graph1 and Graph2 are structurally 80% similar – and then I can somehow print/locate the 20% where they are different in structure, e. g. I work in Python.

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  • $\begingroup$ Hi and welcome to the MathOverflow. Your question is quite interesting, in that it resembles a classification problem: this is something very common in mathematics. Nevertheless tis imprecise: how would you define "structural similarity"? If you don't know what do you want to emphasise and find out od a structure, how could anyone help you by sharing methods to determine this property? $\endgroup$
    – Daniele Tampieri
    Commented yesterday
  • $\begingroup$ Thank you. For example: If a graph was created by copy+paste+modify of another graph, I want to know that. So if a graph has the same edge or node types (possibly even the same subtypes of elements) and is generally structured in the same way, this could indicate this. Also: Are the same nodes/edges at same hierarchy level? Was somewhere one edge added as compared to another graph? I guess I would then also map the elements of the graphs onto another to analyze this? $\endgroup$
    – Possibleble
    Commented yesterday

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