Definition: Two graphs are homeomorphic if they can be made isomorphic by inserting new vertices of degree 2 into edges.

Note: This corresponds to the topological notion since adding or removing degree 2 vertices doesn't change the graph's topology.

This is similar to, but not the same as, homomorphic.

Author: PEB

More information

Eric Weisstein's MathWorld entries for homomorphism and homeomorphism.

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 17 December 2004.
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Cite this as:
Paul E. Black, "homeomorphic", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 17 December 2004. (accessed TODAY) Available from: