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
Ronold Wyeth Percival King100
Willi Jäger100
Dimitris John Bertsimas97
Erol Gelenbe96
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Bart De Moor91
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Wolfgang Karl Härdle85
Rudiger W. Dornbusch85
Olivier Jean Blanchard82
Andrei Nikolayevich Kolmogorov82
David Garvin Moursund82
Selim Grigorievich Krein82
Richard J. Eden81
Stefan Jähnichen81
Sergio Albeverio81

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Sahl 'Isa ibn Yahya al-Masihi227202
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili227202
Abu Mansur al-Hasan ibn Nuh al-Qumri227202
Abu ʿAli al-Husayn (Avicenna) ibn Sina227201
Bahmanyār ibn al-Marzubān227200
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2271991068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī227198
Fakhr al-Dīn Muhammad al-Rēzī227196
Sharaf al-Dīn al-Ṭūsī227196
Qutb al-Dīn Ibrāhīm al-Mīṣrī2271951222
Kamāl al-Dīn Ibn Yūnus227195
Athīr al-Dīn al-Mufaḍḍal al-Abharī2271941264
Nasir al-Dīn al-Ṭūsī227193
Shams al‐Dīn al‐Bukhārī227190
Gregory Chioniadis2271891296
Manuel Bryennios2271881300
Theodore Metochites2271871315
Gregory Palamas2271841316
Nilos Kabasilas2271831363
Demetrios Kydones227182
Elissaeus Judaeus227157
Georgios Plethon Gemistos2271561380, 1393
Basilios Bessarion2271531436
Giovanni Conversini2271441363
Manuel Chrysoloras227144

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
0237935
132599
211950
36814
44721
53543
62714
72207
81810
91499
101215
111043
12901
13766
14667
15569
16518
17430
18351
19331
20300
21244
23241
22240
24177
25170
26159
28130
27127
29101
3088
3179
3269
3365
3461
3561
3659
3742
3936
3833
4233
4529
4128
4027
4327
4623
4422
5221
5419
4918
5115
5314
5013
4712
4812
5512
5611
5711
6010
588
688
617
647
596
636
656
706
726
695
714
734
754
824
623
663
793
813
742
762
772
782
852
1002
1302
671
801
881
901
911
931
951
961
971
1011
1091
1111
1431
1761