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 Havinga143
Pekka Neittaanmäki133
Roger Meyer Temam130
Ramalingam Chellappa127
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston109
Willi Jäger101
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Dimitris John Bertsimas98
Johan Pieter Wibaut97
Erol Gelenbe96
Leonard Salomon Ornstein95
Bart De Moor93
Kurt Mehlhorn93
Rutger Anthony van Santen90
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Wolfgang Karl Härdle85
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein82
Olivier Jean Blanchard82

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Sahl 'Isa ibn Yahya al-Masihi234300
Abu Mansur al-Hasan ibn Nuh al-Qumri234300
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili234300
Abu ʿAli al-Husayn (Avicenna) ibn Sina234299
Bahmanyār ibn al-Marzubān234298
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2342971068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī234296
Fakhr al-Dīn Muhammad al-Rēzī234294
Sharaf al-Dīn al-Ṭūsī234294
Kamāl al-Dīn Ibn Yūnus234293
Qutb al-Dīn Ibrāhīm al-Mīṣrī2342931222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2342921264
Nasir al-Dīn al-Ṭūsī234291
Shams al‐Dīn al‐Bukhārī234288
Gregory Chioniadis2342871296
Manuel Bryennios2342861300
Theodore Metochites2342851315
Gregory Palamas2342821316
Nilos Kabasilas2342811363
Demetrios Kydones234280
Elissaeus Judaeus234255
Georgios Plethon Gemistos2342541380, 1393
Basilios Bessarion2342511436
Manuel Chrysoloras234242
Giovanni Conversini2342421363

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
0244331
133313
212221
36986
44779
53642
62771
72232
81888
91541
101256
111046
12956
13803
14659
15594
16527
17459
18366
19329
20323
22249
21246
23241
24186
25180
26180
28132
27128
29104
30100
3177
3271
3370
3669
3565
3460
3745
3836
3936
4234
4331
4029
4129
4528
4625
4420
5219
4918
5116
5416
5015
5315
4714
5514
4813
5713
5612
6010
589
649
729
618
687
707
596
736
635
655
624
814
824
663
693
743
753
803
712
762
782
792
852
902
932
1012
671
771
881
951
961
971
981
1001
1091
1111
1271
1301
1331
1431
1791