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Identifying & linking common vertices in 2 or more unequal multi-graphs?

POSTED BY: Arno Bosse
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Marco and Vitaliy, thank you both very much for your patient and generous responses. I will have time tomorrow to look at them more carefully.

POSTED BY: Arno Bosse

...friendships forged in fire ;-) @Arno Bosse @Marco Thiel

POSTED BY: Vitaliy Kaurov

Some thoughts to add to Marco's... Let's get a list of many random names:

names = EntityValue[RandomEntity["GivenName", 100], "Name"]

enter image description here

Get two non-intersecting sets:

adAuthors = names[[;; 30]];
adRecipients = names[[-30 ;;]];

Create a symbol that can get 2 random potentially overlapping graphs: 

adGraph := 
  Graph[Thread[
    DirectedEdge[RandomChoice[adAuthors, 40], 
     RandomChoice[adRecipients, 40]]], VertexLabels -> "Name", 
   GraphLayout -> "BipartiteEmbedding", 
   Background -> RandomColor[Hue[_, .5]], ImageSize -> 400];

and get 2 random graphs:

adGraphSAMPLE = {adGraph, adGraph}

enter image description here

See intersections of edges and vertices:

interVert = Intersection @@ (VertexList /@ adGraphSAMPLE)
interEdges = Intersection @@ (EdgeList /@ adGraphSAMPLE)

enter image description here

Visualize in your graphs:

HighlightGraph[#, Join[interVert, interEdges],
   GraphLayout -> "BipartiteEmbedding", VertexLabels -> "Name", 
   GraphHighlightStyle -> "Thick"] & /@ adGraphSAMPLE

enter image description here
POSTED BY: Vitaliy Kaurov

HI Arno,

I am not sure whether this is what you need, but here are some pieces of code. First I create two similar graphs with some common nodes.

adAuthors = {"mary", "peter", "peter", "peter"};
adRecipients = {"jane", "arthur", "diana", "diana"};
adAuthors2 = {"paul", "victor", "mary", "diana", "peter"};
adRecipients2 = {"peter", "mary", "paul", "paul", "alonso"};

We can plot the graphs separately:

adGraph = 
 Graph[Thread[DirectedEdge[adAuthors, adRecipients]], 
  VertexLabels -> Placed["Name", Tooltip]]

and 

adGraph2 = 
 Graph[Thread[DirectedEdge[adAuthors2, adRecipients2]], 
  VertexLabels -> Placed["Name", Tooltip]]

We can user Union to generate a list of all authors and all recipients.

Union[adAuthors, adAuthors2]
(*{"diana", "mary", "paul", "peter", "victor"}*)

and 

Union[adRecipients, adRecipients2]
(*{"alonso", "arthur", "diana", "jane", "mary", "paul", "peter"}*)

We can also plot the joint graph like so:

adGraphjoin = 
 Graph[Thread[DirectedEdge[Join[adAuthors, adAuthors2], Join[adRecipients, adRecipients2]]], 
  VertexLabels -> Placed["Name", Tooltip]]

enter image description here

So a combination of Union and Join functions should do the trick for you.

Best wishes from Aberdeen and thanks again for the great conference/workshop in Oxford, Marco
POSTED BY: Marco Thiel
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