# Logical Data Modeling - Symmetric relationship (bi-directional)

A symmetric relation is a type of binary relation that happens when for all a and b in X

• if a is related to b,
• then b is related to a

In mathematical notation, the relation f between x and y is symmetric when $$y = f(x) \\ x= f(y) \\$$

A relation which is not symmetric is asymmetric.

A symmetric relation is an undirected relationship

A symmetric relation is also known as a bi-directional relation.

## Example

• coauthored a paper with,
• distance between
• is married to
• is co-worker of
• is teammate of

## Representation

### Entity Model

When there is no direction on the association, the relationship is symmetric.

### Set

A symmetric relation in the set of {1,2} would be the set of tuple

<1,2>
<2,1>
<1,1> // reflexive
<2,2> // reflexive


### Visual

The relation between x and y is represented by the gray area. The relation is symmetric when $$y = f(x) \\ x= f(y) \\ b = f(a) \\ a = f(b) \\$$

• Symmetric and reflexive (because the relation y=x (the dotted line) is in the relation)