Glänzel, Wolfgang

Rousseau, Ronald

English

Research Papers in Economics

4
© 2005, International Society for Scientometrics and Informetrics (ISSI)
WOLFGANG GLÄNZEL & RONALD ROUSSEAU:
Erdös Distance and
General Collaboration Distance
For those among you who are not particularly
acquainted with mathematics we recall that Paul
Erdös (Pál Erdõs in Hungarian) is the most profi-
cient mathematician ever. His publication list con-
tains more than 1500 items, which is more than
Euler’s. Erdös was born in Budapest in 1913 and
died in Warsaw in 1996. Because he had more
than 500 collaborators mathematicians started co-
unting the Erdös distance (E-distance for short),
defined as the length of the shortest collaborator
link to Erdös. Erdös himself has E-distance zero;
those mathematicians that have at least one article
published in collaboration with Erdös have E-dis-
tance 1; those that collaborated with a collabo-
rator of Erdös have E-distance 2 and so on.
Clearly if one’s E-distance is 4 or more it
becomes difficult to find out the exact value.
Luckily, since the end of last year MathSciNet has
a special feature allowing one to find out imme-
diately. Actually much more is possible as one can
find out the shortest collaboration distance bet-
ween any two mathematicians who have at least
one article in MathSciNet. One can reach this
feature by doing an author search and then
clicking the “MR CD” button.  Of course, it is pos-
sible that there is no collaboration link between
the two scientists.
B  A LB  J B  AB  QD  CE  LG  WL  FM  BN  MR  R S  A S  H Y  A
Barabasi, AL [4] 0 5 7 76627256166
Bar-Ilan, J [3] 505766 57556556
Bookstein, A [3] 7 50776 69666 677
Burrell, QL [5] 77707678667777
Ding, CHQ [4] 66770568654667
Egghe, L [4] 6 66650685616 67
Glanzel, W [3] 25676608356166
Leimkuhler, FF [6] 77988880687888
Mandelbrot, BB [3] 25666536046246
Newman, MEJ [3] 55665658405567
Rousseau, R [3] 6 6 6 7416 7650677
Schubert, A [3] 15676618256067
Simon, HA [4] 65776668467605
Yablonsky, AI [4] 6 6 7 77768677750
Table 1 ”Pseudo-Erdös distances” among informetricians
Out of curiosity we introduced the names of a
number of informetricians or well-known
scientists in our field (such as Benoit
Mandelbrot and Herbert Simon). Remember
that a prerequisite is that this colleague must
have been active as a mathematician. We
introduced the following names: A.L. Barabasi,
J. Bar-Ilan, A. Bookstein, Q.L. Burrell, C.H.Q.
Ding, L. Egghe, H. Eto, W. Glänzel, S.D. Haitun,
F.F. Leimkuhler, B.B. Mandelbrot, M.E.J.
Newman, D. de Solla Price, R. Rousseau, A.
Schubert, H. S. Sichel, H.A. Simon, M. Thelwall,
and A.I. Yablonsky. All this scientist are present
in the MathSci database. Yet some of them
have no collaborators, or just one who in turn
had no collaborators: these are Eto, Haitun,
Price, Sichel and Thelwall. Consequently they
have no Erdös number within mathematics.
Of course, going out of the field of
mathematics might give them an Erdös
number. For example: as Mike Thelwall has a
joint article with Ronald Rousseau, his Erdös
number is at most four.
Results are presented in the following Table.
Shortest paths passing via Erdös are shown in
bold.  E-distances are shown in square brackets
after the name of the scientist.5
© 2005, International Society for Scientometrics and Informetrics (ISSI)
shorter if all publications are taking into account
as this piece co-authored by Rousseau and
Glänzel illustrates.
 References
http://www-history.mcs.st-and.ac.uk/history/
Mathematicians/Erdos.html
Note that this table is of course symmetric. Recall
that it is said that just six steps separate us from
any other person on the planet (for an acquain-
tances network). Clearly for this subset of infor-
metricians-mathematicians shortest collaboration
distances range from 1 to 9.
The following Figure finally visualizes the
pseudo-Erdös distances in a two-dimensional pro-
jection of our informetric network. Distances
The authors wish to thank Dr. Patrick Glenisson for providing the
graphic presentation of the network of informetricians and Alesia
Zuccala who suggested R.R. to have a closer look at MathSciNet.
Figure 1 Graphic presentation of the network of informetricians established through their mathematical work
therefore do not proportionally show the length
of the above paths. The group consisting of
Thelwall, Eto, Haitun and Sichel is symbolically se-
parated from all other authors of the group since
their distance to all authors is infinite. Also Derek
de Solla Price belongs to this group of isolates.
Authors connected by dotted lines have the
shortest link with each other via Erdös. Leimkuhler
and Bookstein, on one hand, and Rousseau/
Egghe and Schubert/Glänzel/Barabási, on the
other hand, form diametrically opposite authors.
Mandelbrot has the shortest average distance
to other authors in the group (<5), Leimkuhler
the longest (finite) one (>7). The average
distance among all authors of in the group is
about 6. This again substantiates the small world
property since we have to keep in mind that all
distances are established through the authors’
mathematical work alone.  Paths connecting
authors might otherwise become essentially

Erdös Distance and General Collaboration Distance.

https://lirias.kuleuven.be/bitstream/123456789/121856/1/erdos.pdf

Erdös Distance and General Collaboration Distance.

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