Talk:Adjacency matrix

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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.

\begin{pmatrix} 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 1\\ 1 & 0 & 0 & 0\\ 1 & 1 & 0 & 0\\ \end{pmatrix}.

[edit] Properties section

What does one cannot 'hear' the shape of a graph mean? --Bkkbrad 19:53, 16 November 2006 (UTC)

Relative to the Adjacency Matrix example, for those less familiar with this area a small edit would clarify that the matrix listing refers to nodes 1 to 6 in the picture, with node 1 at the top and node 6 at the bottom of the matrix --TopoRubin 16:06, 3 March 2007 (UTC)

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