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I have two random graphs G1 and G2 that I want to join with an edge from a particular vertex vx in G1 to a particular vertex vy in G2. I can't find a way to do it.

Here is my latest code:

(* Generate Two Random Barabasi Albert with order up to 30 *)
go1=RandomInteger[{1,30}];
go2 =RandomInteger[{1,30}];
G1=RandomGraph[BarabasiAlbertGraphDistribution[go1,2],VertexLabels->Automatic];
G2 =RandomGraph[BarabasiAlbertGraphDistribution[go2,2],VertexLabels->Automatic];
(* Perform disjoint union to make one graphy with succesive vertices *)
G=GraphDisjointUnion[G1,G2,VertexLabels->Automatic];
(* one random vertex from each graph G1, and G2 *)
v1=RandomChoice[Range[go1]];
v2=RandomChoice[Range[go1+1,go1+go2,1]];
G =EdgeAdd[G,v1\[UndirectedEdge]v2, PlotLabel->"Random Edge Connection between G1 and G2"]
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You need to join the two graph into a single one before you can add edges between them. Look up GraphDisjointUnion.

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  • $\begingroup$ Ah, yes that is what I was kind of doing by joining the incidence matrices, but this function is much more elegant since the vertices are renumbered automagically. $\endgroup$
    – Phillip D. Neumiller
    Jun 17, 2022 at 12:17
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    $\begingroup$ The IGraph/M package has IGDisjointUnion as well which provides some extra features, such as maintaining the mapping between the vertices of the original graphs and the combined graph. $\endgroup$
    – Szabolcs
    Jun 17, 2022 at 12:19

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