In topology, a branch of mathematics, a graph is a topological space which arises from a usual graph G = {\displaystyle G=} by replacing vertices by points and each edge e = x y ∈ E {\displaystyle e=xy\in E} by a copy of the unit interval I = [ 0, 1 ] {\displaystyle I=[0,1]}, where 0 {\displaystyle 0} is identified with the point associated to x {\displaystyle x} and 1 {\displaystyle 1} with the point associated to y {\displaystyle y}. Wikipedia