# Graph, undirected graph, nonoriented graph

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Graph, undirected graph, nonoriented graph --- граф, неориентированный граф.

A graph consists of a finite set of vertices or nodes $V$, a finite set of edges $E$, and a mapping $Ends$ from $E$ to $V \times V$ assigning to each edge $e$ two, not necessarily distinct, vertices of $V$ (the extremities of $e$). The graph $G$ will be denoted by $G = (V, E, Ends)$ or simply $G = (V, E)$. It is easy to see that an edge $e = (v,w)$ corresponds to an undirected pair $(v,w)$ of vertices. If we consider ordered pairs of vertices $(v,w)$, we say about a directed graph with the set of arcs $A = \{(v,w)\}$.