Homeomorphism (graph theory)

In graph theory, two graphs ${\displaystyle G}$ and ${\displaystyle G'}$ are homeomorphic if there is a graph isomorphism from some subdivision of ${\displaystyle G}$ to some subdivision of ${\displaystyle G'}$. If the edges of a graph are thought of as lines drawn from one vertex to another (as they are usually depicted in diagrams), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if their diagrams are homeomorphic in the topological sense.^[1]