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 Kuo179
Egbert Havinga143
Pekka Neittaanmäki133
Roger Meyer Temam130
Ramalingam Chellappa127
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston109
Willi Jäger101
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Dimitris John Bertsimas98
Johan Pieter Wibaut97
Leonard Salomon Ornstein95
Kurt Mehlhorn94
Bart De Moor93
Erol Gelenbe93
Ludwig Prandtl90
Rutger Anthony van Santen90
Yurii Alekseevich Mitropolsky88
Wolfgang Karl Härdle85
Rudiger W. Dornbusch85
Richard J. Eden82
David Garvin Moursund82
Selim Grigorievich Krein82
Olivier Jean Blanchard82

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili235876
Abu Mansur al-Hasan ibn Nuh al-Qumri235876
Abu Sahl 'Isa ibn Yahya al-Masihi235876
Abu ʿAli al-Husayn (Avicenna) ibn Sina235875
Bahmanyār ibn al-Marzubān235874
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2358731068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī235872
Sharaf al-Dīn al-Ṭūsī235870
Fakhr al-Dīn Muhammad al-Rēzī235870
Kamāl al-Dīn Ibn Yūnus235869
Qutb al-Dīn Ibrāhīm al-Mīṣrī2358691222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2358681264
Nasir al-Dīn al-Ṭūsī235867
Shams al‐Dīn al‐Bukhārī235864
Gregory Chioniadis2358631296
Manuel Bryennios2358621300
Theodore Metochites2358611315
Gregory Palamas2358581316
Nilos Kabasilas2358571363
Demetrios Kydones235856
Elissaeus Judaeus235831
Georgios Plethon Gemistos2358301380, 1393
Basilios Bessarion2358271436
Manuel Chrysoloras235818
Giovanni Conversini2358181363

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
0245595
133502
212273
37031
44794
53668
62777
72238
81892
91542
101260
111053
12962
13814
14649
15604
16534
17460
18369
19330
20323
22252
21249
23237
24190
25182
26177
28136
27131
29105
30103
3177
3276
3669
3365
3565
3461
3744
3938
3836
4234
4331
4029
4128
4527
4625
4421
5220
4919
5017
5416
5115
4714
5314
4813
5513
5613
5712
5810
6410
599
609
728
687
737
616
636
656
706
625
825
663
693
713
743
753
793
803
813
762
782
852
902
932
1012
671
771
881
941
951
971
981
1001
1091
1111
1271
1301
1331
1431
1791