Interactive tool for checking graph homeomorphism and isomorphism. Draw graphs and see if they're equivalent.
- Draw graphs: click to add nodes, drag between nodes for edges, right-click to delete
- Check homeomorphism: see if two graphs have the same topological structure
- Check isomorphism: see if two graphs are structurally identical
- Example graphs: load pre-built examples to explore different scenarios
- Dark mode: toggle between light and dark themes
- Undo/Redo: keyboard shortcuts (Ctrl+Z, Ctrl+Y) for graph edits
- Export: save graphs as JSON or export as PNG image
Two graphs are homeomorphic if one can be transformed into the other by adding or removing degree-2 nodes (nodes with exactly 2 connections). It's about topological equivalence - same "shape" even if they look different.
Isomorphism is stricter - graphs must have identical structure with same number of nodes and edges.
Built with vanilla JavaScript and Cytoscape.js for graph rendering.
The homeomorphism algorithm removes all degree-2 nodes from both graphs, then checks if the simplified versions are isomorphic. The isomorphism checker uses backtracking with degree sequence optimization.
MIT - use it for whatever you want.