Homogeneous relation

In mathematics, a homogeneous relation (also called endorelation) over a set X is a binary relation over X and itself, i.e. it is a subset of the Cartesian product X × X.[1][2][3] This is commonly phrased as "a relation on X"[4] or "a (binary) relation over X".[5][6] An example of a homogeneous relation is the relation of kinship, where the relation is over people.

A homogeneous relation R over a set X may be identified with a directed simple graph permitting loops, or if it is symmetric, with an undirected simple graph permitting loops, where X is the vertex set and R is the edge set (there is an edge from a vertex x to a vertex y if and only if xRy). It is called the adjacency relation of the graph.


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