Incidence Matrix

[Oddnumber]

I need help understanding this matrix. Where does the the top row in the table comes from (i.e. e12,e13,e15 etc) ?

 

[Dr.Peterson]

I need help understanding this matrix. Where does the the top row in the table comes from (i.e. e12,e13,e15 etc) ?
View attachment 35122

It looks like the notation they are using is to name the edge joining vertices v_i and v_k as e_ik.

So vertex v₁ is joined to v₅ by e₁₅, whose weight is 3, and so on.

Did your source never define the notation?

 

[Steven G]

The student ask Where does the the top row in the table comes from?
If there is a direct path from Vi to Vj, then and only then is eij in the top heading.

 

[Oddnumber]

The graph did not indicate where the edges are so it’s confusing. Just curious why it starts from e12 and not from e1?

 

[Dr.Peterson]

The graph did not indicate where the edges are so it’s confusing. Just curious why it starts from e12 and not from e1?

They didn't label the edges, but I would hope that somewhere they have stated their convention. Edges are not labeled with a single subscript (there is no "e₁"!), but with a pair, namely the subscripts of the two vertices they join. This is what I tried to explain:



Where did this come from? If it is from a book, look for whatever they say about the notation for edges.

 

[Oddnumber]

They didn't label the edges, but I would hope that somewhere they have stated their convention. Edges are not labeled with a single subscript (there is no "e₁"!), but with a pair, namely the subscripts of the two vertices they join. This is what I tried to explain:

View attachment 35129

Where did this come from? If it is from a book, look for whatever they say about the notation for edges.

Thank you for helping! Really appreciate your help in explaining this. This comes from one of my lecture slide as an example there is no indication or notation to it. I guess this shows how the edges notations should be represented in a table format.

 

[Dr.Peterson]

Thank you for helping! Really appreciate your help in explaining this. This comes from one of my lecture slide as an example there is no indication or notation to it. I guess this shows how the edges notations should be represented in a table format.

Perhaps it was explained orally while the slide was presented.