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I'm writing a small function to alter a graph in a certain way and was wondering if there is a formal name for the operation. The operation takes two distinct edges, injects a new node between the existing nodes of each edge and then adds an edge between the two new nodes. For example:

add new nodes a and b to the graph
let edge1 = (x,y), let edge2 = (u,v)

delete edge (x,y)
create edges (x,a), (a,y)

delete edge(u,v)
create edges(u,b), (b,v)

create edge (a,b)
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I have seen the construction multiple times, but I have never come across a name for it. – utdiscant Jun 27 '12 at 20:16
I do this a lot and I'd love to know a name for it. In data modelling for databases, this is what you do when resolving many-to-many relationships (see e.g. Informix docs); the ORM term is objectification. But I also see it applied a lot to graphs in general, and always anonymously - e.g. in Wikipedia's bipartite graph article. – reinierpost Jul 22 '13 at 9:29

Your attempt is like subdivision. Actually you used two subdivision and finally you add extra edge between center of subdivision nodes.

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The above method is not a subdivision, since the two new vertices are joined by a new edge. – utdiscant Jun 27 '12 at 20:15
I've edited the answer to reflect this. (question text wasn't clear at first). – user742 Jun 28 '12 at 7:19

No. No, there is not. You can come up with one if you'd like.

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