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 Kuo176
Egbert Havinga143
Roger Meyer Temam130
Pekka Neittaanmäki130
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston109
Alexander Vasil'evich Mikhalëv101
Willi Jäger100
Ronold Wyeth Percival King100
Dimitris John Bertsimas97
Erol Gelenbe96
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Bart De Moor91
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Rutger Anthony van Santen87
Rudiger W. Dornbusch85
Wolfgang Karl Härdle85
Olivier Jean Blanchard82
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein82
David Garvin Moursund82
Richard J. Eden81
Stefan Jähnichen81

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Mansur al-Hasan ibn Nuh al-Qumri227594
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili227594
Abu Sahl 'Isa ibn Yahya al-Masihi227594
Abu ʿAli al-Husayn (Avicenna) ibn Sina227593
Bahmanyār ibn al-Marzubān227592
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2275911068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī227590
Sharaf al-Dīn al-Ṭūsī227588
Fakhr al-Dīn Muhammad al-Rēzī227588
Kamāl al-Dīn Ibn Yūnus227587
Qutb al-Dīn Ibrāhīm al-Mīṣrī2275871222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2275861264
Nasir al-Dīn al-Ṭūsī227585
Shams al‐Dīn al‐Bukhārī227582
Gregory Chioniadis2275811296
Manuel Bryennios2275801300
Theodore Metochites2275791315
Gregory Palamas2275761316
Nilos Kabasilas2275751363
Demetrios Kydones227574
Elissaeus Judaeus227549
Georgios Plethon Gemistos2275481380, 1393
Basilios Bessarion2275451436
Manuel Chrysoloras227536
Giovanni Conversini2275361363

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
0238279
132636
211971
36836
44711
53551
62718
72209
81807
91504
101218
111050
12904
13766
14662
15574
16521
17431
18351
19330
20299
21244
22243
23242
24178
25171
26161
28130
27127
29100
3089
3180
3268
3366
3562
3461
3659
3743
3937
4233
3832
4529
4027
4127
4327
4623
4422
5221
5419
4918
5115
5314
4713
5013
5512
5712
4811
5610
589
609
618
688
647
596
656
706
726
635
695
734
754
824
623
663
713
743
793
813
762
772
782
852
1002
1302
671
801
871
881
901
911
931
951
961
971
1011
1091
1111
1431
1761