edge contraction

In graph theory, an edge contraction is an operation which removes an edge from a graph while simultaneously merging together the two vertices it used to connect. All other edges incident to either of the two vertices become incident to the single merged vertex. More generally, we can contract a set of edges by contracting each of them individually. A similar operation is vertex contraction, where we merge together two or more vertices, removing any edges between two of the vertices being contracted.
See more at Wikipedia.org...