Timeline for Are these three different notions of a graph Laplacian?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 23, 2014 at 2:32 | vote | accept | user6818 | ||
| Nov 30, 2014 at 22:24 | answer | added | Delio Mugnolo | timeline score: 2 | |
| Nov 29, 2014 at 5:56 | answer | added | Son P Nguyen | timeline score: 1 | |
| Nov 29, 2014 at 4:26 | answer | added | Chris Godsil | timeline score: 17 | |
| Nov 29, 2014 at 1:56 | comment | added | Aaron Meyerowitz | $L_2$ is not the same kind of graph Laplacian as $L_1$. When one is going to be using both kinds, it is common to call $L_2$ the normalized Laplacian matrix and $L_1$ the standard Laplacian matrix. With certain exceptions (find them!) a normalized Laplacian is not a standard Laplacian. Read the article to see some common properties. | |
| Nov 29, 2014 at 1:08 | comment | added | user6818 | @AaronMeyerowitz So $L_2$ is not a graph Laplacian - right? | |
| Nov 29, 2014 at 0:22 | comment | added | Aaron Meyerowitz | In the middle option you want the diagonal entries to be $1$ (or $0$ in the case of degree $0$ vertices, if any) The Wikipedia article en.wikipedia.org/wiki/Laplacian_matrix explains the connections. $L_1=L_3$ and $L_2=SL_1S$ where $S=\sqrt{D}$ is the diagonal matrix with (non-negative) entries $\sqrt{\deg(v_i)}.$ | |
| Nov 28, 2014 at 23:02 | comment | added | user6818 | oh - sorry - changed it! | |
| Nov 28, 2014 at 23:02 | comment | added | Qiaochu Yuan | What's a reference for the third? Are you sure you don't want $A$ to be the incidence matrix? | |
| Nov 28, 2014 at 22:58 | history | asked | user6818 | CC BY-SA 3.0 |