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 Kuo175
Egbert Havinga143
Roger Meyer Temam130
Pekka Neittaanmäki129
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston109
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Willi Jäger100
Erol Gelenbe95
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Dimitris John Bertsimas92
Ludwig Prandtl90
Bart De Moor89
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Wolfgang Karl Härdle83
Andrei Nikolayevich Kolmogorov82
Selim Grigorievich Krein82
Olivier Jean Blanchard82
David Garvin Moursund82
Stefan Jähnichen81
Sergio Albeverio81
Richard J. Eden81

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Sahl 'Isa ibn Yahya al-Masihi218825
Abu ʿAli al-Husayn (Avicenna) ibn Sina218824
Bahmanyār ibn al-Marzubān218823
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2188221068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī218821
Sharaf al-Dīn al-Ṭūsī218819
Fakhr al-Dīn Muhammad al-Rēzī218819
Qutb al-Dīn Ibrāhīm al-Mīṣrī2188181222
Kamāl al-Dīn Ibn Yūnus218818
Athīr al-Dīn al-Mufaḍḍal al-Abharī2188171264
Nasir al-Dīn al-Ṭūsī218816
Shams al‐Dīn al‐Bukhārī218813
Gregory Chioniadis2188121296
Manuel Bryennios2188111300
Theodore Metochites2188101315
Gregory Palamas2188071316
Nilos Kabasilas2188061363
Demetrios Kydones218805
Elissaeus Judaeus218780
Georgios Plethon Gemistos2187791380, 1393
Basilios Bessarion2187761436
Giovanni Conversini2187671363
Manuel Chrysoloras218767
Gasparino da Barzizza218766
Guarino da Verona2187661408

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
0231041
131668
211565
36605
44605
53449
62638
72141
81751
91449
101178
11980
12897
13749
14629
15551
16491
17403
18349
19317
20288
22245
21237
23212
24175
25166
26141
27126
28120
29103
3086
3176
3464
3262
3356
3655
3552
3738
3937
3832
4231
4127
4326
4025
4524
4622
4420
5118
5218
5416
4915
5315
4813
5013
5713
4711
5510
5610
609
688
587
617
637
596
646
726
655
695
705
624
824
713
733
753
783
813
672
742
762
772
952
1002
661
791
801
831
851
881
891
901
921
931
1011
1091
1111
1291
1301
1431
1751