In the mathematical discipline of graph theory, an Eulerian orientation is an orientation of the edges in an undirected graph such that each vertex has the same number of incoming edges as outgoing edges. This concept is related to an Eulerian circuit, which is a cycle that passes through every edge of a graph exactly once. The namesake of both terms is Leonhard Euler, who initiated the study of graph theory in 1736 when he proved that an graph contains an Eulerian circuit if and only if the graph is connected and every vertex has even degree.