# Talk:Laplacian matrix

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Field: Applied mathematics

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))

From the literature it looks like only a few electrical engineering type people call this an Admittance Matrix, and everybody else calls it a Laplacian Matrix. Does anyone else have an opinion on this?

Meekohi 01:19, 15 December 2005 (UTC)

I have never seen this called anything but the Laplacian matrix in the mathematics literature. JLeander 18:53, 26 August 2006 (UTC)

## Spectral gap

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)

## fdm

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)