Collaboration graph data

Some Data on the Collaboration Graph

The collaboration graph has researchers as its vertices, with an edge between every two researchers who have published a joint paper (with or without other collaborators). We are particularly interested in the portion of the collaboration graph centered at Paul Erdös. The vertices at a distance 1 from Erdös are said to have Erdös number 1; those at distance 2 are said to have Erdös number 2.

The data on this page is based on the updated lists of March 1, 2007.

Here is the distribution of the number of coauthors with Erdös number 1 for the 8162 people with Erdös number 2.

Mean = 1.51
Standard deviation = 1.27
Median = 1
The histogram is as follows:

 Value   Count
    1   6165  ****************************************************
    2   1083  **********
    3    436  ****
    4    190  **
    5    110  *
    6     55  *
    7     36  *
    8     35  *
    9     29  *
   10      8  *
   11      5  *
   12      4  *
   13      0  
   14      3  *
   15      2  *
   16      0
   17      0
   18      0
   19      1  *

(To see who the outliers in this distribution are, click here.)

Here is the distribution of the number of coauthors with Erdös number 1 for the 511 people with Erdös number 1. In other words, this is the vertex degree data for the subgraph of the collaboration graph induced by people with Erdös number 1.

Mean = 6.28
Standard deviation = 7.66
Median = 4
The histogram is as follows:

 Value   Count	
    0      37  *******************
    1      85  *******************************************
    2      68  **********************************
    3      52  **************************
    4      43  **********************
    5      34  *****************
    6      35  ******************
    7      31  ****************
    8      18  *********
    9      14  *******
   10      12  ******
   11      10  *****
   12      10  *****
   13       7  ****
   14       3  **
   15       7  ****
   16       3  **
   17       3  **
   18       3  **
   19       2  *
   20       1  *
   21       2  *
   22       4  **
   23       0  
   24       3  **
   25       2  *
   26       3  **
   27       0  
   28       0  
   29       5  ***
   30       3  **
   31       1  *
   32       1  *
   33       0
   34       0
   35       1  *
   36       1  *
   37       2  *
   38       0
   39       1  *
   40       0
   41       0
   42       1  *
   43       0
   44       2  *
   45       0
   46       0
   47       0
   48       0
   49       0
   50       0
   51       1  *

(To see who the outliers in this distribution are, click here.)

Here is the distribution of the total number of coauthors for the 511 people with Erdös number 1.

Mean = 30.44
Standard deviation = 33.73
Median = 21
The histogram is as follows:

  Value    Count
   0          6  ***
  1-  5      77  ***************************************
  6- 10      66  *********************************
 11- 15      55  ****************************
 16- 20      47  ************************
 21- 25      42  *********************
 26- 30      43  **********************
 31- 35      31  ****************
 36- 40      16  ********
 41- 45      20  **********
 46- 50      17  *********
 51- 55      11  ******
 56- 60      12  ******
 61- 65       9  *****
 66- 70      10  *****
 71- 75       1  *
 76- 80       7  ****
 81- 85       8  ****
 86- 90       6  ***
 91- 95       7  ****
 96-100       3  **
  ...
101-110       2  *
111-120       3  **
121-130       4  **
131-140       2  *
  ...
  150         1  *
  ...
  153         1  *
  ...
  176         1  *
  ...
  195         1  *
  ...
  279         1  *
  ...
  315         1  *

(To see who the outliers in this distribution are, click here.)

The following data is about the vertex Paul Erdös in the collaboration multigraph. It shows the distribution of the number of papers that Erdös's coauthors have with him. (See the file Erdos0p for details.)

Mean = 3.27
Standard deviation = 6.45
Median = 1
The histogram is as follows:

  Value   Count
     1     307  *******************************
     2      70  *******
     3      37  ****
     4      22  ***
     5      14  **
     6       7  *
     7      13  **
     8       4  *
     9       3  *
    10       3  *
    11       2  *
    12       1  *
    13       0
    14       4  *
    15       2  *
    16       0
    17       0
    18       2  *
    19       2  *
    20       1  *
    21       2  *
    22       1  *
    23       1  *
    24       0
    25       0
    26       0
    27       1  *
    28       1  *
    29       1  *
    30       1  *
    31       0
    32       1  *
    33       0
    34       0
    35       2  *
    ...
    42       1  *
    ...
    50       1  *
    ...
    56       1  *
    ...
    62       1  *

The following histogram shows the number of new coauthors Paul Erdös added each year. (See the file Erdos0d for details.)

  Year    Number of new coauthors
  1934       2  **
  1935       0
  1936       4  ****
  1937       3  ***
  1938       4  ****
  1939       2  **
  1940       1  *
  1941       1  *
  1942       1  *
  1943       3  ***
  1944       1  *
  1945       3  ***
  1946       3  ***
  1947       3  ***
  1948       4  ****
  1949       3  ***
  1950       6  ******
  1951       1  *
  1952       1  *
  1953       5  *****
  1954       2  **
  1955       4  ****
  1956       7  *******
  1957       2  **
  1958       5  *****
  1959       6  ******
  1960       1  *
  1961       4  ****
  1962       4  ****
  1963       7  *******
  1964       7  *******
  1965       7  *******
  1966      10  **********
  1967       3  ***
  1968       2  **
  1969       3  ***
  1970       6  ******
  1971       7  *******
  1972       9  *********
  1973      17  *****************
  1974      13  *************
  1975      17  *****************
  1976      17  *****************
  1977      11  ***********
  1978      14  **************
  1979      10  **********
  1980      13  *************
  1981      12  ************
  1982       3  ***
  1983      17  *****************
  1984       6  ******
  1985      20  ********************
  1986       8  ********
  1987      34  **********************************
  1988      22  **********************
  1989      10  **********
  1990      15  ***************
  1991      14  **************
  1992      12  ************
  1993      10  **********
  1994       9  *********
  1995      10  **********
  1996      15  ***************
  1997      14  **************
  1998       4  ****
  1999      13  *************
  2000       0
  2001       0
  2002       1  *
  2003       1  *
  2004       1  *
  2005       0
  2006       0
  2007       1  *

Click here for a text file of the adjacency lists of the collaboration graph of Paul Erdös’s coauthors, for those who want to do their own further analysis. Please share any results with us!

URL = http://www.oakland.edu/enp/erddata.html
This page was last updated on March 9, 2007.
Return to Erdös Number Project home page.