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 Bertsimas94
Kurt Mehlhorn93
Bart De Moor90
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Wolfgang Karl Härdle85
David Garvin Moursund82
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein82
Olivier Jean Blanchard82
Richard J. Eden81
Stefan Jähnichen81
Sergio Albeverio81

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili223604
Abu Mansur al-Hasan ibn Nuh al-Qumri223604
Abu Sahl 'Isa ibn Yahya al-Masihi223604
Abu ʿAli al-Husayn (Avicenna) ibn Sina223603
Bahmanyār ibn al-Marzubān223602
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2236011068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī223600
Sharaf al-Dīn al-Ṭūsī223598
Fakhr al-Dīn Muhammad al-Rēzī223598
Kamāl al-Dīn Ibn Yūnus223597
Qutb al-Dīn Ibrāhīm al-Mīṣrī2235971222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2235961264
Nasir al-Dīn al-Ṭūsī223595
Shams al‐Dīn al‐Bukhārī223592
Gregory Chioniadis2235911296
Manuel Bryennios2235901300
Theodore Metochites2235891315
Gregory Palamas2235861316
Nilos Kabasilas2235851363
Demetrios Kydones223584
Elissaeus Judaeus223559
Georgios Plethon Gemistos2235581380, 1393
Basilios Bessarion2235551436
Giovanni Conversini2235461363
Manuel Chrysoloras223546

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
0234987
132163
211768
36732
44664
53518
62657
72183
81787
91490
101197
111014
12895
13764
14652
15557
16515
17412
18356
19320
20292
22247
21235
23231
24175
25170
26153
27128
28127
2996
3089
3182
3464
3263
3658
3357
3556
3741
3936
3835
4233
4330
4025
4125
4525
4622
5221
5420
4418
4917
5117
5313
5713
4712
4812
5012
5511
5610
609
689
588
618
647
697
636
595
725
735
654
704
824
623
713
743
783
813
662
752
762
772
792
852
902
1002
1302
671
801
881
931
941
951
961
1011
1091
1111
1431
1761