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I would like to generate the set of all possible, non-isomorphic graphs for a given number of nodes (n) with specified degrees. Such graphs are relatively small, they may have n = 1-8 where the degree of nodes may range from 1-4.

Generated graphs must be allowed to contain loops and multi-edges. Here, multi-edges have a max value of 2, that is any two nodes may be connected to eachother by a maximum of 2 edges, they may also be connected by 1 edge or 0 edges.

E.G. Generate all possible graphs (thay are allowed to contain loops and multi-edges) with 4 nodes (n = 4) where 2 of the nodes have the degree 2 (2-connected) and two of the nodes have the degree 3 (3-connected).

I have worked this out on paper, there should be 11 different graphs.

Is there an efficient way to generate all possible graphs (with restrictions listed above) with n nodes where the degree of each node is specified ?

Thanks!

-Maxwell Day

Christine Tobler
on 24 Nov 2020

Christine Tobler
on 30 Nov 2020

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