# Multigraph : mathematical representation

#### zulfi100

Joined Jun 7, 2012
656
Hi,
I cant understand mathematical representation of multigraph:
A multigraph G = (V,E,f) is composed of a set of vertices V, a set of edges E and a function f: E-> {{vi , vj} :

vi, v j is a member of V and vi is not equal to vj}.

Can somebody please guide me why there is definition of f and what is meant by E-> {{vi , vj}

Zulfi.

#### WBahn

Joined Mar 31, 2012
26,398
You need to look at what functions are -- namely mappings from one set to another set.

#### zulfi100

Joined Jun 7, 2012
656
Thanks for your response. There is only one function 'f' and it is assigning nodes vi & vj to an edge E. I got the answer from another forum.

Zulfi.

#### WBahn

Joined Mar 31, 2012
26,398
It is mapping an edge in the set E to a pair of nodes {vi, vj} in the set of all possible pairs of nodes (they are imposing the constraint that vi can't equal vj, which just means they aren't allowing loops).

You continue to not want to really learn these concepts. Instead, you just want someone on some forum to feed you an answer. That's a lousy way to learn stuff like this and it continually shows in the nature of the questions you keep asking because they almost always reveal a lack of comprehension of the fundamentals that should have been in place well before you ever started looking at the material you are asking about.

#### zulfi100

Joined Jun 7, 2012
656
Hi,
<It is mapping an edge in the set E to a pair of nodes {vi, vj} in the set of all possible pairs of nodes (they are imposing the constraint that vi can't equal vj, which just means they aren't allowing loops).>
Overall your statement is correct because its trying to differentiate between loops & circuits. Loops wont have repeated vertices but circuits can have. I have problem with the word mapping. Maybe you are right (because in maths -> means mapping) but its giving the definition of a function & in programming we use the word assignment and not mapping. Any way thanks for your help, you are my great teacher and i am trying to learn from you.
<
That's a lousy way to learn stuff like this and it continually shows in the nature of the questions you keep asking because they almost always reveal a lack of comprehension of the fundamentals that should have been in place well before you ever started looking at the material you are asking about.>
I am trying to take advantage of the resources on the internet. That's why we have forums. I am not afraid of putting such questions on the forum because its a source of learning for me. Why should i close the doors of learning for me?? Book does not have description. I tried to understand it but i failed. Even if you look at the introduction (opening page) of hw forum, it encourages asking question related to book topics which somebody is not able to understand. Its not related to fundamentals of maths. I am (was) not a mathematics student, though i have studied some mathematics subject but they never teach equation comprehension. I cant understand why are calling it a fundamental thing (i.e 1st year thing) . If you are right then tell me any fundamental cs subject which teaches development (involves ms/phd research work) & understanding of mathematical equations. No teacher teaches it, they just show you the slides containing the equations and many would even skip it.
Sorry if it hurts you.
Zulfi.