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 Kuo181
Egbert Havinga146
Pekka Neittaanmäki133
Roger Meyer Temam130
Ramalingam Chellappa127
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston107
Paul Scholten105
Dimitris John Bertsimas102
Willi Jäger101
Ronold Wyeth Percival King100
Alexander Vasil'evich Mikhalëv99
Johan Pieter Wibaut97
Leonard Salomon Ornstein95
Kurt Mehlhorn94
Erol Gelenbe93
Bart De Moor93
Ludwig Prandtl90
Rutger Anthony van Santen90
Yurii Alekseevich Mitropolsky88
Wolfgang Karl Härdle85
Rudiger W. Dornbusch85
Holm Altenbach85
Michael Irwin Jordan84
David Garvin Moursund82

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Sahl 'Isa ibn Yahya al-Masihi242749
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili242749
Abu Mansur al-Hasan ibn Nuh al-Qumri242749
Abu ʿAli al-Husayn (Avicenna) ibn Sina242748
Bahmanyār ibn al-Marzubān242747
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2427461068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī242745
Fakhr al-Dīn Muhammad al-Rēzī242743
Sharaf al-Dīn al-Ṭūsī242743
Kamāl al-Dīn Ibn Yūnus242742
Qutb al-Dīn Ibrāhīm al-Mīṣrī2427421222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2427411264
Nasir al-Dīn al-Ṭūsī242740
Shams al‐Dīn al‐Bukhārī242737
Gregory Chioniadis2427361296
Manuel Bryennios2427351300
Theodore Metochites2427341315
Gregory Palamas2427311316
Nilos Kabasilas2427301363
Demetrios Kydones242729
Elissaeus Judaeus242704
Georgios Plethon Gemistos2427031380, 1393
Basilios Bessarion2427001436
Giovanni Conversini2426911363
Manuel Chrysoloras242691

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
0252702
134310
212535
37195
44909
53728
62869
72310
81910
91562
101311
111102
12965
13844
14675
15619
16558
17478
18378
19347
20332
21257
22254
23242
25198
24193
26171
28142
27139
30110
29107
3184
3273
3470
3369
3668
3559
3746
3841
3941
4236
4335
4131
4027
4527
4627
4423
5221
5019
4718
4918
4815
5415
5314
5513
5112
5612
5712
5810
6410
609
598
618
637
657
727
686
696
706
746
826
665
735
785
624
753
803
853
672
712
772
792
902
932
761
811
841
881
941
951
971
991
1001
1011
1021
1051
1071
1111
1271
1301
1331
1461
1811