An edge joins two vertices of a graph. If another vertex is introduced onto that edge, it creates two edges, so in the figures below, the insertion of the vertex C has subdivided the edge AB into two edges, namely AC and CB. The extra vertex C is necessarily of degree 2. A subdivision of a graph is a graph modified by the addition of one or more vertices of degree 2 into an existing edge or edges.
![subdivision](Images/oree/doc/10.1093/acref/9780198845355.001.0001/acref-9780198845355-graphic-265-full.gif)