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
Ramalingam Chellappa127
Shlomo Noach (Stephen Ram) Sawilowsky111
Andrew Bernard Whinston109
Alexander Vasil'evich Mikhalëv101
Ronold Wyeth Percival King100
Willi Jäger100
Dimitris John Bertsimas98
Erol Gelenbe96
Leonard Salomon Ornstein95
Kurt Mehlhorn93
Bart De Moor91
Rutger Anthony van Santen90
Ludwig Prandtl90
Yurii Alekseevich Mitropolsky88
Rudiger W. Dornbusch85
Wolfgang Karl Härdle85
Andrei Nikolayevich Kolmogorov82
Olivier Jean Blanchard82
David Garvin Moursund82
Selim Grigorievich Krein82
Richard J. Eden81

Expand to top 75 advisors

Most Descendants

NameDescendantsYear of Degree
Abu Sahl 'Isa ibn Yahya al-Masihi231732
Abu Mansur al-Hasan ibn Nuh al-Qumri231732
Abu Abdallah Al-Husayn ibn Ibrahim al-Natili231732
Abu ʿAli al-Husayn (Avicenna) ibn Sina231731
Bahmanyār ibn al-Marzubān231730
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm al-Khayyām al-Nīsābūrī2317291068
Saraf al-Dīn Muhammad al-Masʿūdī al-Marwazī231728
Sharaf al-Dīn al-Ṭūsī231726
Fakhr al-Dīn Muhammad al-Rēzī231726
Kamāl al-Dīn Ibn Yūnus231725
Qutb al-Dīn Ibrāhīm al-Mīṣrī2317251222
Athīr al-Dīn al-Mufaḍḍal al-Abharī2317241264
Nasir al-Dīn al-Ṭūsī231723
Shams al‐Dīn al‐Bukhārī231720
Gregory Chioniadis2317191296
Manuel Bryennios2317181300
Theodore Metochites2317171315
Gregory Palamas2317141316
Nilos Kabasilas2317131363
Demetrios Kydones231712
Elissaeus Judaeus231687
Georgios Plethon Gemistos2316861380, 1393
Basilios Bessarion2316831436
Giovanni Conversini2316741363
Manuel Chrysoloras231674

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
0241777
132989
212121
36903
44769
53606
62741
72212
81860
91520
101241
111063
12928
13790
14658
15579
16532
17446
18363
19330
20318
22247
23245
21242
24182
25177
26171
28130
27127
29107
3095
3177
3369
3268
3667
3563
3460
3743
3938
3834
4234
4330
4129
4527
4627
4026
4420
5220
4918
5418
5115
4814
5014
5314
4713
5613
5512
5712
6010
588
648
728
687
707
596
616
635
655
624
734
754
824
663
693
713
743
783
803
672
762
792
812
852
902
1002
771
881
911
931
951
961
981
1011
1091
1111
1271
1301
1321
1431
1781