What is the Eulerian circuit in a graph?

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What is the Eulerian circuit in a graph?

An Eulerian circuit in a graph is a path that starts and ends at the same vertex, and passes through every edge of the graph exactly once. In other words, it is a closed walk that includes all the edges of the graph. This concept is named after the Swiss mathematician Leonhard Euler, who first studied it in the 18th century. An Eulerian circuit exists in a graph if and only if the graph is connected and every vertex has an even degree. If a graph has an Eulerian circuit, it is called an Eulerian graph.