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 Neittaanmäki130
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
Olivier Jean Blanchard82
David Garvin Moursund82
Selim Grigorievich Krein82
Stefan Jähnichen81
Sergio Albeverio81
Richard J. Eden81

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Sahl 'Isa ibn Yahya al-Masihi221607
Abu ʿAli al-Husayn (Avicenna) ibn Sina221606
Bahmanyār ibn al-Marzubān221605
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2216041068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī221603
Fakhr al-Dīn Muhammad al-Rēzī221601
Sharaf al-Dīn al-Ṭūsī221601
Kamāl al-Dīn Ibn Yūnus221600
Qutb al-Dīn Ibrāhīm al-Mīṣrī2216001222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2215991264
Nasir al-Dīn al-Ṭūsī221598
Shams al‐Dīn al‐Bukhārī221595
Gregory Chioniadis2215941296
Manuel Bryennios2215931300
Theodore Metochites2215921315
Gregory Palamas2215891316
Nilos Kabasilas2215881363
Demetrios Kydones221587
Elissaeus Judaeus221562
Georgios Plethon Gemistos2215611380, 1393
Basilios Bessarion2215581436
Giovanni Conversini2215491363
Manuel Chrysoloras221549
Gasparino da Barzizza221548
Guarino da Verona2215481408

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
0233223
131919
211683
36672
44638
53504
62636
72171
81768
91472
101187
111002
12896
13759
14631
15558
16505
17404
18353
19321
20292
22243
21233
23224
24176
25171
26145
27127
28121
29101
3086
3180
3465
3262
3356
3655
3553
3742
3835
3935
4231
4328
4127
4025
4525
4621
5221
4419
5418
4916
5115
5315
4713
5013
4812
5712
5510
6810
569
588
608
618
638
596
646
726
695
654
704
734
824
623
713
743
753
783
813
662
762
772
952
1002
1302
671
791
801
831
851
881
891
901
921
931
1011
1091
1111
1431
1751