Talk:Laplacian matrix

message: The text ", with i < j" is redundant and can be omitted. L = B B^\textsf{T} is independent of the direction of the edges. 
KP (talk) 17:18, 7 March 2024 (UTC)
thread_title: Symmetric Laplacian via the incidence matrix

message: The first definition listed for the Laplacian Matrix, L = D-A seems to not match the second definition. With the example graph below, D(1,1) = 4 and A(1,1) = 1 (since there is a loop connecting vertex 1 with itself). Then, if L = D - A, we would have L(1,1) = 4 - 1 = 3. But in fact, L(1,1) =4.
I checked wolfram.com, and it only mentions the second definition. Therefore, I'm removing the definition L = D - A.
(Georgevulov 23:01, 18 August 2007 (UTC)
thread_title: Untitled

message: The article currently states:
:The smallest non-trivial eigenvalue of L is called the spectral gap or Fiedler value.
Yet the article on expander graphs states that the spectral gap is the difference between the two largest eigenvalues of the adjacency matrix. That these two might be the same thing is not obvious, and needs clarification. linas (talk) 23:49, 7 September 2008 (UTC)
thread_title:  Spectral gap 

message: The link to fdm should be disambiguated. I don't know where it should go though. 131.246.194.40 (talk) 08:36, 20 January 2012 (UTC)
thread_title:  fdm 

message: The etymology needs to be included.174.3.125.23 (talk) 06:56, 10 November 2014 (UTC)
thread_title:  Etymology 

message: In the degree matrix definition a directed graph is given as the example. In this the example is the undirected graph. 
I think a note to flag this is important. 
109.144.196.64 (talk) 13:29, 11 August 2015 (UTC)
thread_title:  Inconsistent with degree matrix  

message: I quote: "The name of the random-walk normalized Laplacian comes from the fact that this matrix is simply the transition matrix of a random walker on the graph.". This can't be true, as a transition matrix is nonnegative. --Peleg (talk) 12:50, 27 October 2015 (UTC)
thread_title:  The name of the random-walk normalized Laplacian 

message: The definition of random walk normalized Laplacian is inconsistent with the one given in the beginning. It is also different from the element-wise definition that follows (as D^{-1} A is non negative). It seems that it should be defined as I - D^{-1}A, however, the identity involving L_{sym}, is correct according to the current definition.  — Preceding unsigned comment added by 151.100.102.21 (talk) 16:49, 9 November 2015 (UTC)
thread_title:  Definition of random-walk normalized Laplacian 

message: Substituted at 02:16, 5 May 2016 (UTC)
thread_title: Assessment comment

message: People, MathWorld is not a reliable reference.  It has enough errors that you cannot simply trust it.  (I rarely look at MathWorld but when I do, I find errors fairly often.)  I propose it be removed from this article.  
For the definition of the Laplacian matrix, it is in so many textbooks that it could be treated as common knowledge.  Source less elementary statements, I would say (IMO, but I may be wrong about this).  Zaslav (talk) 22:11, 23 August 2016 (UTC)
thread_title:  Unreliable reference 

message: I don't see anything about edge weights.  To my naïve eyes, the talk about multigraphs comes closest.  Would someone who knows what they are doing add to that section or a new section a discussion about how undirected and directed graphs with edge weights are handled?  Thank you 66.194.253.20 (talk) 13:57, 27 January 2021 (UTC)
thread_title:  Edge weights