Logical Data Modeling - Symmetric relationship (bi-directional)

1 - About

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 <MATH> y = f(x) \\ x= f(y) \\ </MATH>

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.

3 - Example

4 - Representation

4.1 - Entity Model

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

4.2 - 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

4.3 - Visual

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

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

5 - Documentation / Reference


Data Science
Data Analysis
Statistics
Data Science
Linear Algebra Mathematics
Trigonometry

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