# Graph (discrete mathematics)

## Vertices connected in pairs by edges / From Wikipedia, the free encyclopedia

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In discrete mathematics, and more specifically in graph theory, a **graph** is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects are represented by abstractions called *vertices* (also called *nodes* or *points*) and each of the related pairs of vertices is called an *edge* (also called *link* or *line*).^{[1]} Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges.

The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person *A* can shake hands with a person *B* only if *B* also shakes hands with *A*. In contrast, if an edge from a person *A* to a person *B* means that *A* owes money to *B*, then this graph is directed, because owing money is not necessarily reciprocated.

Graphs are the basic subject studied by graph theory. The word "graph" was first used in this sense by J. J. Sylvester in 1878 due to a direct relation between mathematics and chemical structure (what he called a chemico-graphical image).^{[2]}^{[3]}