Edge Coverage

Euler Path & Circuit

Find a path that traverses every edge exactly once. Hierholzer's Algorithm efficiently discovers these trails by finding sub-cycles and merging them.

Time ComplexityO(V + E)

ConditionEven Degrees

Try Interactive Simulator

Hierholzer's Logic

The algorithm uses a stack to build a path until it gets stuck, then backtracks and appends nodes to the circuit as it returns.

Circuit vs Path

A circuit exists if all nodes have even degrees. A path exists if exactly two nodes have odd degrees (start and end).

🖱️ Click to Add • ↔️ Drag to Move • ⌨️ Shift+Drag to Join

Loading Lab...

Edge Coverage

Euler Path & Circuit

Find a path that traverses every edge exactly once. Hierholzer's Algorithm efficiently discovers these trails by finding sub-cycles and merging them.

Time ComplexityO(V + E)

ConditionEven Degrees

Try Interactive Simulator

Hierholzer's Logic

The algorithm uses a stack to build a path until it gets stuck, then backtracks and appends nodes to the circuit as it returns.

Circuit vs Path

A circuit exists if all nodes have even degrees. A path exists if exactly two nodes have odd degrees (start and end).

🖱️ Click to Add • ↔️ Drag to Move • ⌨️ Shift+Drag to Join

Euler Path Circuit

Euler Path Circuit

Euler Path & Circuit

Hierholzer's Logic

Circuit vs Path

Euler Path & Circuit

Hierholzer's Logic

Circuit vs Path