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 Abdallah Al-Husayn ibn Ibrahim al-Natili234296
Abu Sahl 'Isa ibn Yahya al-Masihi234296
Abu Mansur al-Hasan ibn Nuh al-Qumri234296
Abu ʿAli al-Husayn (Avicenna) ibn Sina234295
Bahmanyār ibn al-Marzubān234294
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2342931068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī234292
Fakhr al-Dīn Muhammad al-Rēzī234290
Sharaf al-Dīn al-Ṭūsī234290
Qutb al-Dīn Ibrāhīm al-Mīṣrī2342891222
Kamāl al-Dīn Ibn Yūnus234289
Athīr al-Dīn al-Mufaḍḍal al-Abharī2342881264
Nasir al-Dīn al-Ṭūsī234287
Shams al‐Dīn al‐Bukhārī234284
Gregory Chioniadis2342831296
Manuel Bryennios2342821300
Theodore Metochites2342811315
Gregory Palamas2342781316
Nilos Kabasilas2342771363
Demetrios Kydones234276
Elissaeus Judaeus234251
Georgios Plethon Gemistos2342501380, 1393
Basilios Bessarion2342471436
Manuel Chrysoloras234238
Giovanni Conversini2342381363

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
0244304
133313
212222
36985
44780
53641
62771
72232
81888
91541
101255
111046
12955
13803
14660
15594
16526
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