A graph is simply a network; as such, a graph containing a collection of nodes (or "vertices"), in which pairs of nodes are connected via segments or curves called edges. A sample graph is depicted below, in which nodes are labeled with the integers between 1 and 6.

This graph is undirected, meaning that its edges do not come
equipped with an orientation. For this reason, we may safely use either the notation

The abstract mathematical study of graphs and their properties is called graph theory and dates to 1735, when Leonhard Euler used a graph to demonstrate that there was no way to walk across the seven bridges of Konigsberg (in Prussia), cross each bridge exactly once, and return to one's starting point (see Eulerian cycle).