### Introduction

Eulerian Path are paths that

- Start at some node
- Visit every node exactly once
- And ends

For the above Diagram We can start at some node for example say

We starts at node **D**

The next criteria is Visit every node exactly once

In the above graph we can transverse in any manner. I’m transversing in following manner.

D -> B -> A -> D -> C -> A

So in the above we have an Eulerian path that started at D and ended at A

### Condition

If a graph is connected and have a two node with even degree, than it has an

Eulerian path.

As seen from above example the starting and ending node D and A has an odd degree.

If Graph has all odd degree that graph can’t have a Eulerian Path

### Exception

If all the node is of even degree

For example

The below graph has an Eulerian Path even when all of it’s node is even

Transverse

A -> B -> C -> E -> B -> D -> C -> A

We start and end up at the same node so the node should have a even degree

This is special kind of the Eulerian Path and this is known as **Eulerian Tour**