Is there a name for the problem of turning a bipartite graph into two graphs in the following way? We form one graph from the vertices on the left, such that two vertices are made adjacent if they share a common neighbour on the right; we form the other graph similarly from the vertices on the right.
This pops up, for example, when finding collaboration relationships in a bipartite graph from scientists to papers or actors to movies.
This being a common problem, I wonder if it has a common name, and maybe specific literature on it.