Homogeneous relation

In mathematics, a homogeneous explanation also called endorelation over a category X is the binary relation over X as living as itself, i.e. it is for a subset of the Cartesian product . This is ordinarily phrased as "a explanation on X" or "a binary relation over X". An example of a homogeneous relation is the relation of kinship, where the relation is over people.

Common nature of endorelations add orders, graphs, and equivalences. Specialized studies order theory in addition to graph theory pretend developed apprehension of endorelations. Terminology particular for graph idea is used for description, with an ordinary graph presumed to correspond to a symmetric relation, and a general endorelation corresponding to a directed graph. An endorelation R corresponds to a logical matrix of 0s and 1s, where the expression xRy corresponds to an edge between x and y in the graph, and to a 1 in the square matrix of R. it is for called an adjacency matrix in graph terminology.

Operations

If R is a homogeneous relation over a set X then used to refer to every one of two or more people or matters of the coming after or as a a object that is caused or featured by something else of. is a homogeneous relation over X:

All operations defined in Binary relation § Operations on binary relations also apply to homogeneous relations.