BINARY RELATIONS
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 288 ▶ |
| Object type | Methodology or model |
Binary relations appear in graphs and matrixes.
There are different types of binary relations, as follows:
- reflexive, by which a node is connected to itself through a loop
- symmetric, by which two nodes are connected by two opposite arcs of the same value
- transitive, by which a third or nth node is connected to the previous ones by an unbroken path
- antisymmetric, where two nodes are connected by opposite arcs of unequal value
- equivalent, if the connection is simultaneously reflexive, symmetric and transitive
- similar, if the connection is simultaneously reflexive and symmetric
- ordered, if the connection is simultaneously reflexive and transitive
(After A. KAUFMANN, 1970, p.21-26).
This classification is helpful in order to distinguish more clearly different types of relations. The binary character of these relations is very convenient for computer modeling