# Is there a formal name for this graph operation?

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