homeomorphic graph

In mathematics, two graphs are considered homeomorphic if they can be obtained from the same graph by subdividing its edges. This means that you can transform one graph into the other by adding or removing vertices along the edges, without changing the fundamental connections between vertices.1

A homeomorphism itself is a one-to-one mapping between two sets that is continuous in both directions. In simpler terms, it's a way to deform one shape into another without tearing or gluing, preserving essential topological properties like connectedness. A topological transformation is another term for a homeomorphism.23

A graph can be a diagram representing data, the set of points satisfying a relation, or a collection of vertices and edges. Homeomorphic graphs share the same underlying structure when viewed through the lens of topology.421