**Introduction**

In graph theory, an **Eulerian circuit** is a path that starts from a vertex and passes all edges once (and only **once**) and returns to the same vertex. If the path passes through all edges but does not return to its first place, it is called an **Eulerian path**.

There is no specific software to find the Eulerian circuit, and to find this circuit, the existing algorithms must be coded in one of the programming languages. The **Optimization City** group has developed an online solver for the problem of finding the Eulerian circuit. Below is a guide for using this online solver.

**Instruction of using online solver of the Eulerian circuit**

The GUI of the online solver of this problem is as follows.

**Problem input**

To find the optimal solution to the problem of finding the Eulerian circle, the required inputs are as follows:

**n:** the number of desired graph nodes.

**m:** the number of edges of the desired graph.

**nodei:** is a vector with m+1 components, where the i-th component represents the initial node of the i-th edge.

**nodej:** is a vector with m+1 components, where the i-th component represents the terminal node of the i-th edge.

**Example: **Consider the graph below.

Determine the Euler circuit of the above graph.

**Solution:**

Entering information in the online solver of the euler circuit is as follows

After entering the data, we click on the **RUN** button.

The result of running the algorithm is as follows.

In the output part, it reports the edges that exist in the Euler circuit.