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
Pekka Neittaanmäki130
Roger Meyer Temam130
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston109
Alexander Vasil'evich Mikhalëv101
Willi Jäger100
Ronold Wyeth Percival King100
Erol Gelenbe96
Dimitris John Bertsimas95
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Ludwig Prandtl90
Bart De Moor90
Yurii Alekseevich Mitropolsky88
Wolfgang Karl Härdle85
Rudiger W. Dornbusch85
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Olivier Jean Blanchard82
Selim Grigorievich Krein82
Richard J. Eden81
Sergio Albeverio81
Stefan Jähnichen81

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili225440
Abu Sahl 'Isa ibn Yahya al-Masihi225440
Abu Mansur al-Hasan ibn Nuh al-Qumri225440
Abu ʿAli al-Husayn (Avicenna) ibn Sina225439
Bahmanyār ibn al-Marzubān225438
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2254371068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī225436
Sharaf al-Dīn al-Ṭūsī225434
Fakhr al-Dīn Muhammad al-Rēzī225434
Kamāl al-Dīn Ibn Yūnus225433
Qutb al-Dīn Ibrāhīm al-Mīṣrī2254331222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2254321264
Nasir al-Dīn al-Ṭūsī225431
Shams al‐Dīn al‐Bukhārī225428
Gregory Chioniadis2254271296
Manuel Bryennios2254261300
Theodore Metochites2254251315
Gregory Palamas2254221316
Nilos Kabasilas2254211363
Demetrios Kydones225420
Elissaeus Judaeus225395
Georgios Plethon Gemistos2253941380, 1393
Basilios Bessarion2253911436
Giovanni Conversini2253821363
Manuel Chrysoloras225382

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
0236435
132420
211855
36781
44702
53517
62698
72193
81800
91499
101202
111032
12890
13767
14660
15561
16517
17428
18349
19325
20296
22243
21240
23236
24178
25168
26154
28129
27126
2997
3089
3183
3268
3462
3359
3559
3657
3743
3937
3833
4231
4330
4029
4527
4123
4623
5223
4421
5420
4917
5114
4813
5313
5012
5612
4711
5511
5711
6010
6810
618
648
587
697
596
635
725
654
704
734
824
623
663
713
743
753
793
813
762
772
782
852
902
952
1002
1302
671
801
881
931
961
1011
1091
1111
1431
1761