Graph structure

In July 2016, Cosmin Ionita and Pat Quillen of MathWorks used MATLAB to analyze the Math Genealogy Project graph. At the time, the genealogy graph contained 200,037 vertices. There were 7639 (3.8%) isolated vertices and 1962 components of size two (advisor-advisee pairs where we have no information about the advisor). The largest component of the genealogy graph contained 180,094 vertices, accounting for 90% of all vertices in the graph. The main component has 7323 root vertices (individuals with no advisor) and 137,155 leaves (mathematicians with no students), accounting for 76.2% of the vertices in this component. The next largest component sizes were 81, 50, 47, 34, 34, 33, 31, 31, and 30.

For historical comparisonn, we also have data from June 2010, when 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 (5% of the total). 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 had 4,639 root verticies, i.e., mathematicians for whom the advisor is currently unknown.

Top 25 Advisors

NameStudents
C.-C. Jay Kuo162
Roger Meyer Temam128
Pekka Neittaanmäki123
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston108
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Willi Jäger100
Erol Gelenbe95
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Dimitris John Bertsimas87
Bart De Moor86
Rudiger W. Dornbusch85
David Garvin Moursund82
Selim Grigorievich Krein82
Olivier Jean Blanchard82
Andrei Nikolayevich Kolmogorov82
Stefan Jähnichen81
Bruce Ramon Vogeli80
Richard J. Eden80
Sergio Albeverio80
Arnold Zellner79

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Sharaf al-Dīn al-Ṭūsī193720
Kamāl al-Dīn Ibn Yūnus193719
Nasir al-Dīn al-Ṭūsī193718
Shams al‐Dīn al‐Bukhārī193717
Gregory Chioniadis1937161296
Manuel Bryennios193715
Theodore Metochites1937141315
Gregory Palamas193712
Nilos Kabasilas1937111363
Demetrios Kydones193710
Elissaeus Judaeus193687
Georgios Plethon Gemistos1936861380, 1393
Basilios Bessarion1936831436
Manuel Chrysoloras193656
Guarino da Verona1936551408
Vittorino da Feltre1936541416
Theodoros Gazes1936501433
Johannes Argyropoulos1936321444
Jan Standonck1936281474
Jan Standonck1936281490
Cristoforo Landino193601
Marsilio Ficino1936011462
Angelo Poliziano1936001477
Moses Perez193598
Scipione Fortiguerra1935981493

Nonplanarity

The Mathematics Genealogy Project graph is nonplanar. Thanks to Professor Ezra Brown of Virginia Tech for assisting in finding the subdivision of K3,3 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.

K_{3,3} in the Genealogy graph

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 StudentsFrequency
0209964
128872
210374
35951
44207
53128
62402
71953
81515
91275
101051
11897
12798
13678
14550
15479
16425
17393
18315
19256
20251
22220
21206
23173
24152
25139
26117
27114
28106
2996
3080
3156
3356
3252
3452
3546
3635
3734
3829
3929
4127
4227
4327
4024
4418
5218
4516
4916
4615
4815
4714
5113
5312
5011
5511
5711
5410
569
609
587
617
636
696
625
645
594
654
684
724
824
703
733
773
803
672
712
752
762
952
1002
661
741
781
791
811
851
861
871
881
901
931
1011
1081
1111
1231
1281
1621