Edge Contraction in a Graph
The contraction of an edge of a graph is the graph obtained by identifying the vertices and , and replacing them with a single vertex ; any edges that were incident to or are redirected to . This operation plays a major role in the analysis of graph coloring. You can chose a random graph and then choose which vertex is to be contracted. The graph at the top shows the edge to be contracted and the graph at the bottom shows the graph after the contraction.