# Statisical Summaries

### Here is the distribution of the number of coauthors with Erdös number 1 for the 12,600 people with Erdös number 2.

• Mean = 1.47

• Standard deviation = 1.24

• Median = 1

• The frequency distribution is as follows:

• Value Count

• 1 9784

• 2 1551

• 3 599

• 4 275

• 5 132

• 6 89

• 7 56

• 8 37

• 9 30

• 10 17

• 11 11

• 12 7

• 13 4

• 14 2

• 15 4

• 16 0

• 17 1

• 18 0

• 19 1

(Here are the outliers in this distribution.)

### Here is the distribution of the number of coauthors with Erdös number 1 for the 512 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 = 6.63

• Standard deviation = 8.14

• Median = 4

• The frequency distribution is as follows:

Value Count

0 37

1 82

2 65

3 50

4 41

5 35

6 39

7 24

8 20

9 17

10 12

11 13

12 9

13 4

14 6

15 7

16 6

17 4

18 2

19 4

20 1

21 3

22 1

23 0

24 2

25 2

26 2

27 3

28 2

29 2

30 3

31 2

32 0

33 1

34 1

35 2

36 0

37 0

38 0

39 1

40 2

41 0

42 0

43 1

44 2

45 0

46 0

47 1

48 0

49 0

50 0

51 0

52 0

53 0

54 0

55 0

56 0

57 0

58 1

(Here are the outliers in this distribution.)

### Here is the distribution of the total number of coauthors (other than Erdös) for the 512 people with Erdös number 1.

• Mean = 42.74

• Standard deviation = 53.17

• Median = 27

• The frequency distribution is as follows:

Value Count

0 6

1 13

2 13

3 18

4 9

5 9

6- 10 61

11- 15 56

16- 20 32

21- 25 41

26- 30 30

31- 35 30

36- 40 24

41- 45 19

46- 50 16

51- 55 15

56- 60 15

61- 65 6

66- 70 5

71- 75 8

76- 80 7

81- 85 5

86- 90 5

91- 95 7

96-100 5

101-110 13

111-120 5

121-130 5

131-140 4

141-150 8

151-160 5

161-170 2

171-180 1

181-190 4

191-200 0

201-250 3

262 1

267 1

277 1

278 1

282 1

315 1

520 1

(Here are the outliers in this distribution.)

### The following data are 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 = 6.44

• Median = 1

• The histogram is as follows:

Value Count

1 309 *******************************

2 70 *******

3 38 ****

4 22 ***

5 14 **

6 7 *

7 12 **

8 5 *

9 3 *

10 2 *

11 3 *

12 1 *

13 0

14 4 *

15 2 *

16 0

17 0

18 2 *

19 2 *

20 1 *

21 2 *

22 0

23 2

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 *

2015 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!