Erdős number

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Alice writes a paper together with Erdős and thus receives the Erdős number 1. If Bob never worked with Erdős, but with Alice, then he receives the Erdős number 2.

The Erdős number indicates the distance in the graph of the co-authorship related to the mathematician Paul Erdős . In the graph, the authors related to journalism are represented as nodes, between each of which there is an edge if they have jointly authored a publication . The definition of the Erdős number goes back in all probability to the analyst Casper Goffman (1913-2006), who wrote a scientific article on the collaborations of Erdős as early as 1969 . The title of the article was: And what is your Erdős number? (in German: "And what is your Erdős number?").

According to the definition of the Erdős number, Paul Erdős himself has the Erdős number 0, all co-authors with whom he has published have the Erdős number 1. Authors who published with Paul Erdős co-authors (but not with Erdős himself) have the Erdős number 2 etc. If no connection in this form to a person can be established, their Erdős number is infinite. It turns out that the Erdős number of most people is either infinite or very small. The 268,000 people for whom the Erdős number project was able to determine a finite value have an average Erdős number of 4.65. This is mainly due to the fact that Erdős worked in many sub-areas of mathematics and published together with over 500 different scientists. The basis for calculating the respective Erdős number are bibliographic databases that are administered and regularly updated by the Erdős number project . On this basis, the Erdős number of each author can be determined.

The calculation of the Erdős number is of no importance for the individual mathematician, even if the graph of the co-authorship of Erdős is often used as an example for graphs of networks in scientific publications. In general terms, the Erdős number illustrates an aspect of social networks that is also dealt with in the context of the small world phenomenon . Other relationships can be defined analogously; the most prominent similar example is the Bacon number , which is defined through collaborations among actors.

table

The following table shows how many mathematicians have which Erdős number (based on an evaluation of the Math Reviews database, as of July 29, 2015):

Erdős number people
0 1
1 504
2 6593
3 33605
4th 83642
5 87760
6th 40014
7th 11591
8th 3146
9 819
10 244
11 68
12 23
13 5
Total: 268015

In addition, there are 133,000 authors in the database who have an infinite Erdős number (80,000 of them are people who have not written any articles with co-authors).

Erdős numbers outside of mathematics

Thanks to the cooperation of Erdős or his co-authors in other departments, many non-mathematicians also have a finite Erdős number, e.g. B. the physicist Albert Einstein (2), the linguist Noam Chomsky (4) or the German Chancellor and PhD physicist Angela Merkel (5).

Trivia

William Tozier, a mathematician with the Erdős number 4, offered a co-authorship in an auction on eBay in 2004 , enabling the winner to purchase the Erdős number 5. The auction was won by a Spanish mathematician with a bid of $ 1,031. However, the latter subsequently refused to pay and stated that he had only submitted his bid to prevent the auction, which he perceived as a farce.

Web links

Individual evidence

  1. ↑ Casper Goffman: And what is your Erdős number? . In: American Mathematical Monthly . 76, 1969.
  2. ↑ a b c Facts about Erdös Numbers and the Collaboration Graph. The distribution of Erdös numbers. In: The Erdös Number Project. Oakland University, September 15, 2010, accessed October 3, 2010 (July 2004 database).
  3. ↑ Paths to Erdös . In: The Erdös Number Project . Oakland University.
  4. ^ Clifford A. Pickover : A Passion for Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality . Wiley, 2011, ISBN 978-1-118-04607-4 , p. 33 excerpt (Google) .
  5. ↑ Erica Klarreich: Theorems for Sale . In: Science News , Vol. 165, No. 24 (Jun. 12, 2004), pp. 376-377, JSTOR 4015267 .