# Graph

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

**Context:**- It can range from being an Undirected Graph to being a Directed Graph (if the Graph Edges are Arcs).
- It can be an Empty Graph.
- It can range from being a Cyclic Graph to being an Acyclic Graph.
- It can range from being a Simple Graph to being a Complex Graph.
- It can range from being an Unlabeled Graph to being a Labeled Graph.
- It can range from being a Connected Graph to being a Disconnected Graph.
- It can range from being a Finite Graph to being an Infinite Graph.
- It can range from being a Static Graph to being a Dynamic Graph.
- It can be a Subgraph to some other Graph.
- It can be a Bipartite Graph.
- It can be a Probabilistic Graph.
- It can be in an Graph Isomorphic Relation with another Graph.
- It can be represented by a graph data structure.
- It can be illustrated by a Graph Drawing System.
- It can have a Graph Property/Graph Statistic, such as:
- It can be a task input to a [Graph Analysis Task]].

**Example(s):**`<graph>digraph {n1 -> n2; n2 -> n3; n3 -> n1; }</graph>`

- A Dynamic Network where information flows over time.
- a Conceptual Graph.
- a string (it can be represented with a Rooted Directed Graph).
- a Concept Space??
- a string

**Counter-Example(s):**- a Multiset.
- a Hyperplane within some Space.
- an Infographic.

**See:**Mathematical Entity.

## 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.

- QUOTE:In mathematics, a

### 2011

- (Jensen, 2011) ⇒ Tommy R. Jensen. (2011). “Graphs.” In: (Sammut & Webb, 2011) p.479

### 2009

- (WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=graph
- S: (n) graph, graphical record (a visual representation of the relations between certain quantities plotted with reference to a set of axes)

### 2004

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