Timeline for Spectrum of adjacency matrix of block graph
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 22, 2017 at 13:06 | vote | accept | Ranveer Singh | ||
| Jun 10, 2016 at 13:36 | vote | accept | Ranveer Singh | ||
| May 22, 2017 at 13:06 | |||||
| Jun 10, 2016 at 4:56 | comment | added | Ranveer Singh | In social networks negative edge denotes hatred or enemity between two nodes. In adjacency matrix of signed graph/network we put (i,j)th entry equals to 1 if edge between nodes i & j is postive. Similary (i,j)th entry equals to -1 if edge between nodes i & j is negative otherwise (i,j)th entry is 0. | |
| Jun 9, 2016 at 16:55 | comment | added | Aaron Meyerowitz | What do you mean by a positive or negative edge? An eigenvector of the usual adjacency matrix assigns values to the vertices. | |
| Jun 9, 2016 at 9:07 | comment | added | Ranveer Singh | I am working on signed graphs. There is concept in signed graphs that, if a signed graph can be clustered in groups of nodes such that each edge inside a group is positive while each edge between any two group is negative we call such signed graph a balanced graph. Eigenvalues of these graphs describes useful properties. Above problem also having groups(here complete sub-graphs) connected in chain by an edge to its adjacent groups. Although my interest is in when the connecting edge is negative, but I think I can solve it if you help me considering it as positive edge. | |
| Jun 8, 2016 at 20:42 | answer | added | Zahra Taheri | timeline score: 3 | |
| Jun 8, 2016 at 20:09 | comment | added | Aaron Meyerowitz | Where did this come from? A path of length $d=2m-2$ fits this description with $n_1=n_m=1$ and otherwise $n_i=2.$ The $d$ eigenvalues are well known and nice, but not trivial. For your graph you would have $n$ eigenvalues. You can see that all but about $d$ are equal to $-1$ (add an identity matrix and consider the rank). The other $d$ or so are not as nice as for a path. | |
| Jun 8, 2016 at 16:49 | history | asked | Ranveer Singh | CC BY-SA 3.0 |