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
Erol Gelenbe96
Leonard Salomon Ornstein95
Bart De Moor93
Kurt Mehlhorn93
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 Mansur al-Hasan ibn Nuh al-Qumri235686
Abu Sahl 'Isa ibn Yahya al-Masihi235686
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili235686
Abu ʿAli al-Husayn (Avicenna) ibn Sina235685
Bahmanyār ibn al-Marzubān235684
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2356831068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī235682
Fakhr al-Dīn Muhammad al-Rēzī235680
Sharaf al-Dīn al-Ṭūsī235680
Qutb al-Dīn Ibrāhīm al-Mīṣrī2356791222
Kamāl al-Dīn Ibn Yūnus235679
Athīr al-Dīn al-Mufaḍḍal al-Abharī2356781264
Nasir al-Dīn al-Ṭūsī235677
Shams al‐Dīn al‐Bukhārī235674
Gregory Chioniadis2356731296
Manuel Bryennios2356721300
Theodore Metochites2356711315
Gregory Palamas2356681316
Nilos Kabasilas2356671363
Demetrios Kydones235666
Elissaeus Judaeus235641
Georgios Plethon Gemistos2356401380, 1393
Basilios Bessarion2356371436
Manuel Chrysoloras235628
Giovanni Conversini2356281363

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
0245405
133479
212264
37025
44789
53669
62777
72238
81891
91539
101259
111055
12960
13817
14645
15602
16536
17462
18367
19330
20324
22251
21249
23238
24190
25182
26179
28136
27129
29103
30102
3177
3276
3669
3365
3565
3461
3744
3938
3836
4235
4331
4129
4028
4527
4625
4420
5220
4919
5016
5416
5115
4714
5314
5614
4813
5513
5712
5810
6410
609
598
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
951
961
971
981
1001
1091
1111
1271
1301
1331
1431
1791