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

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Mansur al-Hasan ibn Nuh al-Qumri225221
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili225221
Abu Sahl 'Isa ibn Yahya al-Masihi225221
Abu ʿAli al-Husayn (Avicenna) ibn Sina225220
Bahmanyār ibn al-Marzubān225219
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2252181068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī225217
Sharaf al-Dīn al-Ṭūsī225215
Fakhr al-Dīn Muhammad al-Rēzī225215
Qutb al-Dīn Ibrāhīm al-Mīṣrī2252141222
Kamāl al-Dīn Ibn Yūnus225214
Athīr al-Dīn al-Mufaḍḍal al-Abharī2252131264
Nasir al-Dīn al-Ṭūsī225212
Shams al‐Dīn al‐Bukhārī225209
Gregory Chioniadis2252081296
Manuel Bryennios2252071300
Theodore Metochites2252061315
Gregory Palamas2252031316
Nilos Kabasilas2252021363
Demetrios Kydones225201
Elissaeus Judaeus225176
Georgios Plethon Gemistos2251751380, 1393
Basilios Bessarion2251721436
Manuel Chrysoloras225163
Giovanni Conversini2251631363

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
0236300
132393
211838
36771
44700
53522
62693
72192
81800
91497
101203
111032
12888
13770
14659
15557
16518
17426
18350
19324
20296
22243
21241
23237
24177
25169
26153
28129
27126
2998
3088
3183
3268
3462
3359
3559
3657
3743
3937
3833
4232
4331
4029
4527
4123
5223
4622
5421
4420
4917
5114
4813
5313
5012
5612
4711
5711
5510
6010
6810
618
648
587
697
596
635
725
654
704
734
824
623
713
743
753
793
813
662
762
772
782
852
902
952
1002
1302
671
801
881
931
961
1011
1091
1111
1431
1761