A topological graph is simple unlabeled graph whose connectivity is considered purely on the basis of topological equivalence, so that two edges 
and 
joined by a node 
of degree two are considered equivalent to the single edge
.
Two graphs are called homeomorphic graphs if they are isomorphic when considered as topological graphs, i.e., if there exists an isomorphism from a graph subdivision of one to a subdivision of the other.
The numbers of inequivalent topological graphs among connected graphs on 
, 2, ... vertices are 1, 1, 2, 6, ....
Similarly, the numbers of inequivalent topological graphs among connected graphs on 
,
2, ... edges are 1, 1, 3, 5, ....
