Timeline for The distance distribution of graphs
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| Oct 29, 2021 at 18:34 | answer | added | R W | timeline score: 1 | |
| Oct 29, 2021 at 15:20 | answer | added | Eytan | timeline score: 1 | |
| Dec 21, 2020 at 22:03 | answer | added | Matthieu Latapy | timeline score: 2 | |
| S Dec 16, 2020 at 15:54 | history | bounty ended | Hans-Peter Stricker | ||
| S Dec 16, 2020 at 15:54 | history | notice removed | Hans-Peter Stricker | ||
| Dec 16, 2020 at 9:16 | vote | accept | Hans-Peter Stricker | ||
| Dec 15, 2020 at 14:41 | answer | added | Carlo Beenakker | timeline score: 3 | |
| Dec 15, 2020 at 13:44 | history | edited | Hans-Peter Stricker | CC BY-SA 4.0 |
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| Dec 15, 2020 at 13:11 | history | edited | Hans-Peter Stricker | CC BY-SA 4.0 |
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| S Dec 15, 2020 at 11:56 | history | bounty started | Hans-Peter Stricker | ||
| S Dec 15, 2020 at 11:56 | history | notice added | Hans-Peter Stricker | Authoritative reference needed | |
| Sep 14, 2020 at 11:31 | comment | added | Hans-Peter Stricker | Let us continue this discussion in chat. | |
| Sep 13, 2020 at 9:08 | comment | added | JimN | Are you referring to your first picture? Yes, that shows there is a difference in distance distribution and degree distribution. But can you show two 6-regular graphs with different distance distributions where one distribution (correctly) predicts something like contagion-spreading better than the other? If not, the branching factor of 6 is still going to be the main measure an epidemiologist will use to estimate a disease's r-naught value. | |
| Sep 13, 2020 at 8:46 | comment | added | Hans-Peter Stricker | My first and main example: The spreading of contagious diseases depends of course on the degree distribution of the underlying contact network, but maybe even more on the distance distribution (which in turn correlates with the degree distribution). | |
| Sep 13, 2020 at 8:35 | comment | added | JimN | good luck! To address your question, clearly the distance distribution provides more information than a degree distribution, but can you find examples of when the distance distribution explains any phenomenon in real networks that the degree-distribution is insufficient to detect or predict? The distance distribution may provide more info, but at the cost of a more complex measure. There needs to be incentive to use a complex measure when a degree distribution would do. | |
| Sep 13, 2020 at 8:21 | comment | added | Hans-Peter Stricker | I'll do my best. | |
| Sep 13, 2020 at 8:13 | comment | added | JimN | To make a random partial k-tree:start with a large clique,store all cliques of size k, choose one uniformly at random and make a new node adj to that chosen k-clique.This creates a clique of size (k+1), so you store more new k-cliques. Now delete some small number of edges(this destroys a number of k-cliques). Again, add a new vertex adj to a uniformly-chosen existing k-clique and repeat. I have a paper on higher-order structures in random models where we tried to argue the importance of going beyond degree distribution: tinyurl.com/yxna36n7 , and (partial) k-trees had the desirables | |
| Sep 13, 2020 at 8:07 | comment | added | JimN | random k-trees share the expected/desirable power law distribution in node degrees, like Barabasi-Albert, but B-A lacks higher-order statistics like clique/clustering distributions that k-trees also exhibit. And there are other higher-order distributions that k-trees have which match real-world distributions (like edge embeddedness and overlapping clusters) which other models have. | |
| Sep 13, 2020 at 7:56 | comment | added | Hans-Peter Stricker | @JimN: I added diagrams for a random $4$-regular graph. A Watts-Strogatz graph and a power-law graph (Barabasi-Albert) is to come. | |
| Sep 13, 2020 at 7:55 | history | edited | Hans-Peter Stricker | CC BY-SA 4.0 |
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| Sep 13, 2020 at 7:17 | comment | added | JimN | can you generate those diagrams from the random graph distributions which have been studied specifically for their degree distribution: random k-trees and Barabasi-Albert models, maybe also the small-world model of Watts-Strogatz? | |
| Sep 10, 2020 at 13:07 | history | asked | Hans-Peter Stricker | CC BY-SA 4.0 |