other names: contraction of a graph along the edge
    graph theory:
    Let G = (V, E) is a graph and e = xy is an edge between vertices x and y (e`in`E; x,y`in`V).
    With contraction of edge e into a new vertex z(`in V_0`) we obtained a new graph H = (`V_0`, `E_0`), where vertex set `V_0` is vertex set V without vertices x and y and with new vertex z (`V_0` = V - {x, y} + {z}).
    Edge set `E_0` is edge set E without edge e (or all edges between x and y) and z becomes adjacent to all the former neighbours of x and of y.
    Shortly, we can say that result of contraction of edge e is deleting of the edge and identifying its endpoints.
    
    
    Contraction of edge is usually denoted as H = G/e.
    
    If graph is imbedded in a surface, then the contraction of graph along any edge may be realized in the surface.
    The genus of a graph is at least as large as the genus of any graph obtained by a sequence of contractions applied to it.