# Top 50 Advisors

# Most Descendants

# Frequency Counts

The table below indicates the values of number of students for mathematicians in our database along with the number of mathematicians having that many students.

Number of Students | Frequency |
---|---|

0 | 138167 |

1 | 17884 |

2 | 6878 |

3 | 3967 |

4 | 2782 |

5 | 2036 |

6 | 1542 |

7 | 1207 |

8 | 979 |

9 | 845 |

10 | 626 |

11 | 560 |

12 | 485 |

13 | 414 |

14 | 375 |

15 | 291 |

16 | 270 |

17 | 234 |

18 | 171 |

19 | 167 |

21 | 153 |

20 | 141 |

22 | 137 |

23 | 105 |

24 | 99 |

26 | 79 |

25 | 74 |

28 | 63 |

27 | 62 |

29 | 48 |

32 | 43 |

31 | 39 |

34 | 38 |

30 | 36 |

35 | 33 |

33 | 23 |

38 | 23 |

40 | 22 |

41 | 21 |

36 | 19 |

42 | 18 |

39 | 16 |

37 | 14 |

43 | 14 |

52 | 14 |

45 | 12 |

55 | 11 |

51 | 9 |

53 | 9 |

48 | 8 |

50 | 8 |

59 | 8 |

44 | 7 |

49 | 7 |

46 | 6 |

47 | 6 |

56 | 6 |

54 | 4 |

58 | 4 |

67 | 4 |

81 | 4 |

60 | 3 |

62 | 3 |

65 | 3 |

57 | 2 |

61 | 2 |

63 | 2 |

64 | 2 |

71 | 2 |

77 | 2 |

87 | 2 |

66 | 1 |

68 | 1 |

70 | 1 |

72 | 1 |

73 | 1 |

74 | 1 |

75 | 1 |

76 | 1 |

78 | 1 |

80 | 1 |

82 | 1 |

85 | 1 |

92 | 1 |

95 | 1 |

97 | 1 |

100 | 1 |

112 | 1 |

125 | 1 |

# Nonplanarity

The Mathematics Genealogy Project graph is nonplanar. Thanks to Professor Ezra Brown of Virginia Tech for assisting in finding the subdivision of *K*_{3,3} depicted below. The green vertices form one color class and the yellow ones form the other. Interestingly, Gauß is the only vertex that needs to be connected by paths with more than one edge.

# Graph structure

In June 2010, Professor David Joyner of the United States Naval Academy asked for data from our database to analyze it as a graph. At the time, the genealogy graph had 142,688 vertices. Of these, 7,190 were isolated vertices. The largest component had 121,424 vertices (85% of the total number). The next largest component had 128 vertices. The next largest component sizes were 79, 61, 45, and 42. The most frequent size of a nontrivial component was 2; there were 1937 components of size 2. The component with 121,424 vertices has 4,639 root verticies, i.e., mathematicians for whom the advisor is currently unknown.