Talk:Adjacency matrix

message: 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)
replies: text: This is correct, although multigraphs have a multiset of edges. Derrick Coetzee 00:25, 2 Oct 2004 (UTC)

text: That's a great idea. Deco 01:39, 21 Mar 2005 (UTC)

text: \begin{pmatrix}
0 & 1 & 0 & 1\\
0 & 0 & 1 & 1\\
1 & 0 & 0 & 0\\
1 & 1 & 0 & 0\\
\end{pmatrix}.
The statement about det(I-A) is definitely wrong.  For an infinite set of counter-examples, consider the adjacency matrices of complete graphs of 3 or more vertices.  They all have determinant I-A not equal to 0, so are invertible, but they also all contain cycles, whether treated as directed or undirected graphs. Cdsmith (talk) 15:31, 1 May 2008 (UTC)
thread_title:  Untitled 

message: Could someone with the necessary references start a history section?  First known use of adjacency matrices, etc. I've searched around online and can't find anything on it's first known/documented use, or which specific cultures used it. Mojodaddy (talk) 14:23, 17 May 2009 (UTC)
thread_title: History section

message: I don't know if it's right, but I added the name 'one-hop connectivity matrix' for adjacency matrix.  I'm not sure, but this might be only used in network communication (ie, IEEE) circles.  Rhetth (talk) 00:11, 8 December 2009 (UTC)
thread_title:  one-hop connectivity matrix? 

message: Adjacency matrices are a central concept in all applications of network science. In network science, it is standard to define adjacency matrices of directed graphs such that a_{ij}=1 indicates an edge from j to i. This is relevant for dynamical systems, where \dot x = Ax describes a simple and widely studied model for the spread of information, disease, etc. I think this info should be included in this section, so I am proposing the following version:
The adjacency matrix of a directed graph can be asymmetric. One can define the adjacency matrix of a directed graph either such that 
# a non-zero element  indicates an edge from  to  or 
# it indicates an edge from  to . 
The former definition is commonly used in graph theory. The latter is common in most applied sciences (e.g., dynamical systems, physics, network science) where  is sometimes used to describe linear dynamics on graphs ..
Using the the first definition, the in-degrees of a vertex can be computed by summing the entries of the corresponding column and the out-degree of vertex by summing the entries of the corresponding row. When using the second definition, the in-degree of a vertex is given by the corresponding row sum and the out-degree is given by the corresponding column sum.
Labeled graph	Adjacency matrix
Directed Cayley graph of S4	
Coordinates are 0–23.
As the graph is directed, the matrix is not necessarily symmetric.
Aliceschwarze (talk) 04:34, 19 June 2020 (UTC)
replies: text: I also think this is a good addition. I was going to suggest something like this in any event. --Bill Cherowitzo  (talk) 17:10, 19 June 2020 (UTC)
thread_title:  Adjusting "directed graph" section to address discrepancies in interdisciplinary research