We say that a graph $G$ is homeomorphic to graph $H$ if the realization $R(G)$ of $G$ is topologically homeomorphic to $R(H)$ or, equivalently, $G$ and $H$ have isomorphic subdivisions.

Adapted with permission of the author from Modern Graph Theory by Béla Bollobás, published by Springer-Verlag New York, Inc., 1998.