# Search of Eulerian cycle

## Eulerian cycle

Eulerian cycle, or circuit is a closed path which visits every edge of a graph just once.

## Search algorithm

Graphonline.ru uses search algorithm based on cycles.

*Let’s consider the general case, the case of oriented multigraph, possibly with self-loops. Moreover, we assume that there is a eulerian path in the graph and it consists of one vertex at least. In order to find the eulerian trail we will take into account that a eulerian path is the aggregation of all simple cycles of the graph. Consequently, our task is to find all the cycles effectively and combine them into one, effectively as well. *

Besides, before searching for a cycle, the service checks whether a cycle exists or not. In this regard there is a search of vertices degree.

You may find more detailed information about the algorithm in Wikipedia.

The implementation of the algorithm in C++ may be found in our repository on GitHub: The implementation of Eulerian trail search in Graphoffline.

## How to use

- Create a graph.
- Select “Find Eulerian cycle” in the menu bar.