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 Kuo178
Egbert Havinga143
Pekka Neittaanmäki132
Roger Meyer Temam130
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston109
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Willi Jäger100
Dimitris John Bertsimas97
Erol Gelenbe96
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Bart De Moor91
Ludwig Prandtl90
Rutger Anthony van Santen90
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Wolfgang Karl Härdle85
Selim Grigorievich Krein82
Andrei Nikolayevich Kolmogorov82
Olivier Jean Blanchard82
David Garvin Moursund82
Richard J. Eden81
Stefan Jähnichen81

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili229366
Abu Sahl 'Isa ibn Yahya al-Masihi229366
Abu Mansur al-Hasan ibn Nuh al-Qumri229366
Abu ʿAli al-Husayn (Avicenna) ibn Sina229365
Bahmanyār ibn al-Marzubān229364
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2293631068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī229362
Fakhr al-Dīn Muhammad al-Rēzī229360
Sharaf al-Dīn al-Ṭūsī229360
Qutb al-Dīn Ibrāhīm al-Mīṣrī2293591222
Kamāl al-Dīn Ibn Yūnus229359
Athīr al-Dīn al-Mufaḍḍal al-Abharī2293581264
Nasir al-Dīn al-Ṭūsī229357
Shams al‐Dīn al‐Bukhārī229354
Gregory Chioniadis2293531296
Manuel Bryennios2293521300
Theodore Metochites2293511315
Gregory Palamas2293481316
Nilos Kabasilas2293471363
Demetrios Kydones229346
Elissaeus Judaeus229321
Georgios Plethon Gemistos2293201380, 1393
Basilios Bessarion2293171436
Giovanni Conversini2293081363
Manuel Chrysoloras229308

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
0239598
132733
212026
36879
44729
53563
62709
72230
81829
91513
101223
111052
12915
13774
14659
15575
16531
17431
18358
19337
20306
22246
23242
21241
24180
25173
26168
28131
27124
29103
3090
3178
3269
3369
3663
3562
3460
3743
3937
3833
4232
4129
4329
4529
4026
4623
4421
5220
5419
4917
5115
5315
5014
4713
4813
5512
5712
5611
5810
609
688
617
647
727
706
595
635
655
695
624
734
754
824
663
743
783
803
672
712
762
792
812
852
902
1002
771
881
911
931
951
961
971
1011
1091
1111
1301
1321
1431
1781