# Graph

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A graph is an abstract entity composed of a set of graph nodes and a graph edge relation (between the graph nodes).

## References

### 2012

• http://en.wikipedia.org/wiki/Graph_%28mathematics%29
• QUOTE:In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.

The edges may be directed (asymmetric) or undirected (symmetric). For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this is an undirected graph, because if person A shook hands with person B, then person B also shook hands with person A. On the other hand, if the vertices represent people at a party, and there is an edge from person A to person B when person A knows of person B, then this graph is directed, because knowing of someone is not necessarily a symmetric relation (that is, one person knowing of another person does not necessarily imply the reverse; for example, many fans may know of a celebrity, but the celebrity is unlikely to know of all their fans). This latter type of graph is called a directed graph and the edges are called directed edges or arcs.

Vertices are also called nodes or points, and edges are also called lines. Graphs are the basic subject studied by graph theory. The word "graph" was first used in this sense by J.J. Sylvester in 1878.

### 2004

• Jonathan L. Gross, and Jay Yellen. (2004). “Handbook of Graph Theory." CRC Press.