# 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.