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 Havinga141
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
Yurii Alekseevich Mitropolsky88
Bart De Moor88
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-Masihi218356
Abu ʿAli al-Husayn (Avicenna) ibn Sina218355
Bahmanyār ibn al-Marzubān218354
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2183531068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī218352
Sharaf al-Dīn al-Ṭūsī218350
Fakhr al-Dīn Muhammad al-Rēzī218350
Qutb al-Dīn Ibrāhīm al-Mīṣrī2183491222
Kamāl al-Dīn Ibn Yūnus218349
Athīr al-Dīn al-Mufaḍḍal al-Abharī2183481264
Nasir al-Dīn al-Ṭūsī218347
Shams al‐Dīn al‐Bukhārī218344
Gregory Chioniadis2183431296
Manuel Bryennios2183421300
Theodore Metochites2183411315
Gregory Palamas2183381316
Nilos Kabasilas2183371363
Demetrios Kydones218336
Elissaeus Judaeus218311
Georgios Plethon Gemistos2183101380, 1393
Basilios Bessarion2183071436
Manuel Chrysoloras218298
Giovanni Conversini2182981363
Gasparino da Barzizza218297
Guarino da Verona2182971408

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
0230657
131573
211547
36572
44602
53446
62634
72137
81746
91449
101176
11975
12904
13744
14628
15547
16492
17405
18344
19317
20286
22248
21236
23206
24176
25168
26142
27124
28120
29102
3087
3175
3464
3262
3356
3656
3551
3737
3935
3833
4231
4127
4326
4025
4523
4622
4420
5118
5218
4916
5416
5315
4813
5713
5012
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
882
952
1002
661
791
801
831
851
901
921
931
1011
1091
1111
1291
1301
1411
1751