Timeline for The diameter of the Erdös component of the collaboration graph
Current License: CC BY-SA 3.0
12 events
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| May 9, 2023 at 14:32 | comment | added | The Amplitwist |
The link to sciencedirect.com is broken, but the article can be found at doi:10.1016/S0378-8733(00)00023-X.
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| May 15, 2017 at 10:52 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
added 16 characters in body
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| May 15, 2017 at 10:26 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Image link broken; now fixed. ő vs ö.
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| May 22, 2011 at 1:02 | comment | added | Joseph O'Rourke | @Mark: Stimulating questions! Perhaps prior to Erdös there was never such a level of collaboration, which, for example, required air travel. | |
| May 21, 2011 at 20:57 | comment | added | Mark Bennet | One question which occurs to me in relation to this is of generation - there are some people today, not unrelated to the clique above, who are having a major influence on the shape of mathematics to come. Who will be the equivalent of Erdös, whose graph will be featured in 20 years time? And what other influences are there than those traced by such a graph (key textbooks, for example). And who would you pick out in the generation before Erdös? Or does the graph and concept work for a generation because the definition and documentation of influence belongs to a specific generation? | |
| Nov 13, 2010 at 11:39 | comment | added | user6976 | @Joseph: The growth of the collaboration graph, like any other large social network, may be approximated by some formal rules. Some "coarse" parameters of the network should be possible to predict. For example, will the diameter grow in time? At what speed? Will large highly connected clusters of nodes with relatively few outside edges exist for long time or will each of them break down after some number of steps (years), etc. You can check that the Erdös component of the graph actually contains all Kyoto prize winners (and all Fields medal, Wolff prize, Abel prize, etc. winners). | |
| Nov 11, 2010 at 20:24 | comment | added | Joseph O'Rourke | Laszlo Lovasz (in the clique above) just received the Kyoto Prize! | |
| Nov 10, 2010 at 23:47 | comment | added | Joseph O'Rourke | @Mark, p.176: "The diameter of the large component in graph $E'$ is 12 with three diametric pairs of vertices..." Not that it matters. Re predicting the future of the math community: I assume you are kidding! Regardless, collaboration may be stronger in Erdös-fields than in other areas of mathematics. | |
| Nov 10, 2010 at 22:57 | comment | added | user6976 | @Joseph: Thanks for sending me the paper by email. I thought that 12 in the paper was the diameter of the Erdös component. In principle, it could be that for appropriately chosen parameters in "my" model (described in the question) one can get similar results. Then we would be able to predict the future structure of the mathematics community. | |
| Nov 10, 2010 at 20:46 | comment | added | Joseph O'Rourke | @Mark: There were 17 connected components (after removing the Erdös-root!). One of them was large: 6045 authors. The diameter of that component was 12. They do not seem to report the diameter of the connected graph, but it might be implied by data in their tables. | |
| Nov 10, 2010 at 20:37 | comment | added | user6976 | @Joseph: Thanks! I did not know about this article. Do they consider the diameter also? I wonder if it was smaller or larger than 23 in 2000. I did not find it in the paper yet. | |
| Nov 10, 2010 at 20:28 | history | answered | Joseph O'Rourke | CC BY-SA 2.5 |