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 Kuo169
Roger Meyer Temam130
Pekka Neittaanmäki125
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston108
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Willi Jäger100
Erol Gelenbe95
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Dimitris John Bertsimas91
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Bart De Moor86
Rudiger W. Dornbusch85
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein82
Wolfgang Karl Härdle82
Olivier Jean Blanchard82
David Garvin Moursund82
Stefan Jähnichen81
Sergio Albeverio81
Richard J. Eden80
Bruce Ramon Vogeli80

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu ʿAli al-Husayn (Avicenna) ibn Sina211332
Bahmanyār ibn al-Marzubān211331
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2113301068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī211329
Fakhr al-Dīn Muhammad al-Rēzī211327
Sharaf al-Dīn al-Ṭūsī211327
Kamāl al-Dīn Ibn Yūnus211326
Qutb al-Dīn Ibrāhīm al-Mīṣrī2113261222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2113251264
Nasir al-Dīn al-Ṭūsī211324
Shams al‐Dīn al‐Bukhārī211321
Gregory Chioniadis2113201296
Manuel Bryennios2113191300
Theodore Metochites2113181315
Gregory Palamas2113151316
Nilos Kabasilas2113141363
Demetrios Kydones211313
Elissaeus Judaeus211288
Georgios Plethon Gemistos2112871380, 1393
Basilios Bessarion2112841436
Giovanni Conversini211275
Manuel Chrysoloras211275
Gasparino da Barzizza211274
Guarino da Verona2112741408
Vittorino da Feltre2112731416

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
0224006
130728
211216
36368
44505
53338
62582
72119
81648
91414
101126
11952
12879
13719
14607
15531
16469
17411
18331
19302
20271
22236
21229
23187
24169
25167
26131
28118
27117
29103
3076
3169
3257
3457
3356
3651
3550
3736
3935
3830
4126
4226
4025
4325
4423
4520
4920
4618
5217
5116
5014
5313
5413
4812
4711
5611
5510
5710
6010
588
618
597
637
646
686
655
695
725
745
825
704
623
783
672
712
732
772
802
812
952
1002
751
761
791
851
861
881
901
911
931
1011
1081
1111
1251
1301
1691