distibution-of-degrees-in-the-collaboration-graph-of-the-second-kind

This table shows the distribution of the number of coauthors for the 401,445 authors in the Mathematical Reviews database when we consider only papers with exactly two authors. For example, 16,426 different mathematicians have exactly 3 coauthors under this restriction. In other words, this table gives the distribution of the degrees of the vertices in C', the collaboration graph of the second kind.

number of coauthors        count
        0                 166381
        1                 145872
        2                  34337
        3                  16426
        4                   9913
        5                   6670
        6                   4643
        7                   3529
        8                   2611
        9                   2032
       10                   1585
       11                   1303
       12                   1046
       13                    825
       14                    702
       15                    551
       16                    450
       17                    377
       18                    350
       19                    273
       20                    232
       21                    199
       22                    150
       23                    127
       24                    113
       25                    105
       26                     90
       27                     83
       28                     50
       29                     50
       30                     40
       31                     43
       32                     29
       33                     32
       34                     15
       35                     20
       36                     16
       37                     20
       38                     18
       39                     18
       40                     19
       41                      6
       42                      9
       43                      3
       44                     14
       45                      5
       46                      7
       47                      6
       48                      4
       49                      6
       50                      6
       51                      2
       52                      3
       53                      1
       54                      2
       56                      2
       57                      4
       58                      3
       60                      1
       61                      2
       62                      1
       64                      1
       65                      2
       70                      1
       74                      1
       77                      1
       79                      1
       81                      1
       92                      1
       94                      1
      121                      1
      124                      1
      230                      1

Of course the last line represents Paul Erdös: 230 people have an Erdös number of the second kind of 1, compared to over 500 people with an Erdös number of the first kind of 1.