A symmetric relation is a relation 
on a set 
such that for every 
and 
in 
we have 
iff 
. Symmetric relations on 
elements correspond to rooted simple
graphs on 
vertices, with diagonal pairs represented by edges incident to the root
vertex.
Symmetric Relation
See also
Relation, Rooted GraphExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Symmetric Relation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SymmetricRelation.html