Timeline for Antipodal vertices in spectral graph embeddings
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 18, 2020 at 8:52 | comment | added | M. Winter | @AntoineLabelle My evidence is that it holds for all the graphs I have checken (e.g. the skeletons of regular polytopes, but also many others). | |
| Jul 18, 2020 at 8:48 | comment | added | M. Winter | @AntoineLabelle My intuition comes from spectral embeddings of $G$, where you assign points in Euclidean space to the vertices of $G$, and you do this by somehow using the eigenvectors of $G$ to some eigenvalue. It seems to be common intuition, that the $\theta_2$-embedding is "as expanded as possible" (imagine the vertices as repelling each other, but the edges keeping them together, and then the $\theta_2$-embedding is an equilibrium configuration under these condition). And to be as expanded as possible, it is plausible that antipodal vertices are embedded opposite to each other. | |
| Jul 18, 2020 at 1:50 | comment | added | Antoine Labelle | Do you have any evidence/heuristics for why this should hold in some cases? Also what is special about $\theta_2$? | |
| Jul 3, 2020 at 8:37 | history | edited | M. Winter | CC BY-SA 4.0 |
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| Jul 3, 2020 at 8:31 | history | edited | M. Winter | CC BY-SA 4.0 |
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| Jul 3, 2020 at 8:26 | history | asked | M. Winter | CC BY-SA 4.0 |