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-Natili234633
Abu Sahl 'Isa ibn Yahya al-Masihi234633
Abu Mansur al-Hasan ibn Nuh al-Qumri234633
Abu ʿAli al-Husayn (Avicenna) ibn Sina234632
Bahmanyār ibn al-Marzubān234631
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2346301068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī234629
Fakhr al-Dīn Muhammad al-Rēzī234627
Sharaf al-Dīn al-Ṭūsī234627
Qutb al-Dīn Ibrāhīm al-Mīṣrī2346261222
Kamāl al-Dīn Ibn Yūnus234626
Athīr al-Dīn al-Mufaḍḍal al-Abharī2346251264
Nasir al-Dīn al-Ṭūsī234624
Shams al‐Dīn al‐Bukhārī234621
Gregory Chioniadis2346201296
Manuel Bryennios2346191300
Theodore Metochites2346181315
Gregory Palamas2346151316
Nilos Kabasilas2346141363
Demetrios Kydones234613
Elissaeus Judaeus234588
Georgios Plethon Gemistos2345871380, 1393
Basilios Bessarion2345841436
Giovanni Conversini2345751363
Manuel Chrysoloras234575

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
0244586
133366
212227
36992
44773
53648
62773
72238
81889
91536
101261
111044
12963
13806
14655
15595
16531
17458
18366
19327
20323
22249
21247
23242
24186
25181
26179
28132
27129
29103
30101
3178
3272
3670
3367
3565
3461
3745
3937
3835
4234
4331
4029
4129
4528
4625
4420
5219
4918
5116
5416
5315
4714
4814
5014
5514
5713
5612
6010
589
649
729
618
687
596
656
706
736
635
624
814
824
663
693
713
743
753
803
762
782
792
852
902
932
1012
671
771
881
951
961
971
981
1001
1091
1111
1271
1301
1331
1431
1791