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
Willi Jäger100
Ronold Wyeth Percival King100
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-Masihi220097
Abu ʿAli al-Husayn (Avicenna) ibn Sina220096
Bahmanyār ibn al-Marzubān220095
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2200941068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī220093
Sharaf al-Dīn al-Ṭūsī220091
Fakhr al-Dīn Muhammad al-Rēzī220091
Kamāl al-Dīn Ibn Yūnus220090
Qutb al-Dīn Ibrāhīm al-Mīṣrī2200901222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2200891264
Nasir al-Dīn al-Ṭūsī220088
Shams al‐Dīn al‐Bukhārī220085
Gregory Chioniadis2200841296
Manuel Bryennios2200831300
Theodore Metochites2200821315
Gregory Palamas2200791316
Nilos Kabasilas2200781363
Demetrios Kydones220077
Elissaeus Judaeus220052
Georgios Plethon Gemistos2200511380, 1393
Basilios Bessarion2200481436
Manuel Chrysoloras220039
Giovanni Conversini2200391363
Gasparino da Barzizza220038
Guarino da Verona2200381408

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
0231970
131807
211614
36644
44609
53477
62633
72152
81765
91457
101177
11987
12896
13755
14630
15557
16496
17404
18349
19319
20290
22242
21239
23218
24176
25167
26145
27126
28120
29102
3087
3177
3465
3263
3655
3354
3552
3741
3935
3832
4230
4328
4026
4126
4525
4622
5220
4419
5417
5116
4915
5315
4813
5013
5713
4712
5510
569
608
618
688
587
637
727
596
646
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