Adjacency matrices - real matrices or tables?

  • Thread starter toofle
  • Start date
  • #1
toofle
20
0
A graph can be represented by an adjacency matrix but how is that a real mathematical matrix and not just a table?
A matrix is part of an equation system Ax=B but what is x and B in this case if A is the adjacency matrix?

For example Google does PageRank with Eigenvalues but what would different operations on an adjacency matrix mean, why is it valid to compute eigenvalues and eigenvectors on an adjacency matrix?
Like taking the determinant of an adjacency matrix, what information do we get?
 

Answers and Replies

  • #2
micromass
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
22,178
3,305
A matrix and a table are the exact same thing. A matrix is just a fancy name for a table.

And no, a matrix does need to be part of an equation Ax=b. It can be part of it, but it doesn't need to be.
 
  • #3
pessimist
33
0
The adjacency matrix is as named, a matrix. After all when you want to find the number of walks from one vertex to another you multiply the matrix to itself using matrix multiplication.
 
  • #4
AlephZero
Science Advisor
Homework Helper
7,025
297
Like taking the determinant of an adjacency matrix, what information do we get?

You can certainly give sensible interpretations to some matrix operations on adjacency matrices - addition and multiplication for example.

The fact that you can think of other operations that seem to be meaningless is irrelevant. It's hard to think what "information" you would get from finding the inverse tangent of the number of people in a room, but that doesn't mean that the integers, or trigonometry, have no practical uses.
 

Suggested for: Adjacency matrices - real matrices or tables?

MHB Matrices
  • Last Post
Replies
1
Views
233
  • Last Post
Replies
11
Views
1K
  • Last Post
Replies
5
Views
603
  • Last Post
Replies
1
Views
182
  • Last Post
Replies
3
Views
863
Replies
9
Views
328
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
0
Views
379
Replies
9
Views
433
Top