Talk:Adjacency matrix
I removed
The modified adjacency matrix is generated by replacing all entries greater than 1 in the adjacency matrix by 1.
from the article. The edges in graphs are defined as a set, so it is not possible that an edge (vi,vj) is contained more than once. I think the adjacency matrix should be a (0,1)-matrix and perhaps in a subsection someone could extend this definition to count the number of edges two vertices share.MathMartin 18:56, 25 Sep 2004 (UTC)
- This is correct, although multigraphs have a multiset of edges. Derrick Coetzee 00:25, 2 Oct 2004 (UTC)
Maybe the example graph can contain a self loop, to show how it can be represented into the adjacency matrix.
- That's a great idea. Deco 01:39, 21 Mar 2005 (UTC)
Most software packages show a binary adjacency matrix, even on the diagonal. But loops are always counted twice, and some books show an adjacency matrix like this one, with 2 on the diagonal...
I don't think the information about the relationship between the invertibility of I-A and the presence of directed cycles in the graph is correct. For example, if the adjacency matrix of a directed graph is like the one below, the graph both contains a cycle and has invertible I-A.
