# Graph Edge

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A graph edge is a 2-tuple of graph nodes that are in a (true) graph edge relation.

**AKA:**Network Link.**Context:**- It can be expressed as a pair of Graph Nodes: (
*u,v*). - It can range from being an Undirected Graph Edge (e.g. {
*u,v*}) to being a Directed Graph Edge (e.g. <*u,v*>). - It can have a Graph Edge Attribute (and be a Labeled Graph Edge if the Data Attribute has a Value).
- It can range from being a Weighted Edge (for a weighted graph) to being an Unweighted Edger
- It can be represented by a Graph Edge Record.

- It can be expressed as a pair of Graph Nodes: (
**Example(s):**- a Tree Graph Edge.
- an edge in a triangle.

**Counter-Example(s):****See:**Graph path, Graph Link Mining, Graph Mapping, Symmetric Relation.

## References

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/graph_(mathematics) Retrieved:2014-11-24.
- In mathematics, and more specifically in graph theory, a graph is a representation of a set of objects where some pairs of 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 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 is an undirected graph, because if person A shook hands with person B, then person B also shook hands with person A. In contrast, if there is an edge from person A to person B when person A knows of person B, then this graph is directed, because knowledge of someone is not necessarily a symmetric relation (that is, one person knowing 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*arcs*or*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.^{[1]}

- In mathematics, and more specifically in graph theory, a graph is a representation of a set of objects where some pairs of objects are connected by links. The interconnected objects are represented by mathematical abstractions called

- ↑ See: * J. J. Sylvester (February 7, 1878) "Chemistry and algebra,"
*Nature*,**17**: 284. From page 284: "Every invariant and covariant thus becomes expressible by a*graph*precisely identical with a Kekuléan diagram or chemicograph." * J. J. Sylvester (1878) "On an application of the new atomic theory to the graphical representation of the invariants and covariants of binary quantics, — with three appendices,"*American Journal of Mathematics, Pure and Applied*,**1**(1) : 64-90. The term "graph" first appears in this paper on page 65.

### 2009

- (WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=link
- S: (n) link, nexus (the means of connection between things linked in series)
- S: (n) link, linkup, tie, tie-in (a fastener that serves to join or connect) "the walls are held together with metal links placed in the wet mortar during construction"
- S: (n) connection, link, connectedness (the state of being connected) "the connection between church and state is inescapable"
- S: (n) connection, connexion, link (a connecting shape)
- S: (n) link (a unit of length equal to 1/100 of a chain)
- S: (n) link ((computing) an instruction that connects one part of a program or an element on a list to another program or list)
- S: (n) liaison, link, contact, inter-group communication (a channel for communication between groups) "he provided a liaison with the guerrillas"
- S: (n) radio link, link (a two-way radio communication system (usually microwave); part of a more extensive telecommunication network)
- S: (n) link, data link (an interconnecting circuit between two or more locations for the purpose of transmitting and receiving data)
- S: (v) associate, tie in, relate, link, colligate, link up, connect (make a logical or causal connection) "I cannot connect these two pieces of evidence in my mind"; "colligate these facts"; "I cannot relate these events at all"
- S: (v) connect, link, tie, link up (connect, fasten, or put together two or more pieces) "Can you connect the two loudspeakers?"; "Tie the ropes together"; "Link arms"
- S: (v) connect, link, link up, join, unite (be or become joined or united or linked) "The two streets connect to become a highway"; "Our paths joined"; "The travelers linked up again at the airport"
- S: (v) yoke, link (link with or as with a yoke) "yoke the oxen together"