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 Kuo179
Egbert Havinga144
Pekka Neittaanmäki133
Roger Meyer Temam130
Ramalingam Chellappa127
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston108
Dimitris John Bertsimas101
Willi Jäger101
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv100
Johan Pieter Wibaut97
Leonard Salomon Ornstein95
Kurt Mehlhorn94
Bart De Moor93
Erol Gelenbe93
Ludwig Prandtl90
Rutger Anthony van Santen90
Yurii Alekseevich Mitropolsky88
Wolfgang Karl Härdle85
Rudiger W. Dornbusch85
Johan F. A. K. van Benthem82
Richard J. Eden82
David Garvin Moursund82
Selim Grigorievich Krein82

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Sahl 'Isa ibn Yahya al-Masihi238087
Abu Mansur al-Hasan ibn Nuh al-Qumri238087
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili238087
Abu ʿAli al-Husayn (Avicenna) ibn Sina238086
Bahmanyār ibn al-Marzubān238085
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2380841068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī238083
Fakhr al-Dīn Muhammad al-Rēzī238081
Sharaf al-Dīn al-Ṭūsī238081
Qutb al-Dīn Ibrāhīm al-Mīṣrī2380801222
Kamāl al-Dīn Ibn Yūnus238080
Athīr al-Dīn al-Mufaḍḍal al-Abharī2380791264
Nasir al-Dīn al-Ṭūsī238078
Shams al‐Dīn al‐Bukhārī238075
Gregory Chioniadis2380741296
Manuel Bryennios2380731300
Theodore Metochites2380721315
Gregory Palamas2380691316
Nilos Kabasilas2380681363
Demetrios Kydones238067
Elissaeus Judaeus238042
Georgios Plethon Gemistos2380411380, 1393
Basilios Bessarion2380381436
Manuel Chrysoloras238029
Giovanni Conversini2380291363

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
0247243
133674
212337
37092
44811
53679
62796
72272
81878
91555
101261
111069
12970
13815
14661
15600
16537
17467
18370
19339
20327
22257
21249
23231
24192
25185
26180
27133
28133
29105
30105
3183
3272
3669
3366
3564
3463
3744
3840
3937
4235
4031
4331
4129
4528
4625
4422
5221
5019
4918
5416
4715
5314
4813
5113
5513
5612
5712
5810
6010
6410
599
727
737
616
636
656
686
706
826
625
694
744
663
713
753
793
803
762
782
812
852
902
932
1002
1012
671
771
881
941
951
971
1081
1111
1271
1301
1331
1441
1791