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WOLFRAM|DEMONSTRATIONS PROJECT

Relations and Graphs

size of the set

size of the relation

any

amount needed

choose a type of relation

reflexive

any

yes

symmetric

any

yes

transitive

any

yes

antisymmetric

any

yes

total order

any

yes

function

any

yes

permutation

any

yes

connected

any

yes

acyclic

any

yes

simple

any

yes

There are 16 relations of this type.



◂

▸



A relation on a set

can be described by a 0-1 square matrix where a 1 at row

and column

means that

is related to

. If the size of

, the total number of relations is

. There are several types of relations and this Demonstration allows you to combine choices from the ten most common ones. You can choose

n=1,2,3

, the size of the relation (i.e., the number of 1's in the matrix) and the amount of relations you want to see using the slide viewer. The Demonstration then presents a slide view containing each matrix (if there are any) and its graph (two vertices

and

being connected if there is a 1 at position

in the matrix).

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