In
graph theory, two graphs
and
are
homeomorphic if there is a
graph isomorphism from some
subdivision of
to some
subdivision of
. If the edges of a graph are thought of as lines drawn from one vertex to another (as they are usually depicted in illustrations), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if they are
homeomorphic in the sense in which the term is used in
topology.