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Community detection on elite mathematicians’ collaboration network

Yurui Huang

Yurui Huang

Department of Statistics and Data science, Southern University of Science and TechnologyShenzhen, China
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Huang, Yurui
, 
Zimo Wang

Zimo Wang

Department of Statistics and Data science, Southern University of Science and TechnologyShenzhen, China
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Wang, Zimo
, 
Chaolin Tian

Chaolin Tian

Department of Statistics and Data science, Southern University of Science and TechnologyShenzhen, China
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Tian, Chaolin
 und 
Yifang Ma

Yifang Ma

Department of Statistics and Data science, Southern University of Science and TechnologyShenzhen, China
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Ma, Yifang
  
19. Nov. 2024
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Artikel-Kategorie: Research Papers
Online veröffentlicht: 19. Nov. 2024
Seitenbereich: 1 - 23
Eingereicht: 25. Juli 2023
Akzeptiert: 22. Nov. 2023
DOI: https://doi.org/10.2478/jdis-2024-0026
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© 2024 Yurui Huang et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

Data characteristics of mathematicians.
Data characteristics of mathematicians.

Figure 2.

Network characteristics.
Network characteristics.

Figure 3.

Four centrality metrics were computed within communities identified by both GMM and Infomap, and subsequently compared between awardees and other mathematicians. The metrics assessed were: (a), (e) Betweenness; (b), (f) Closeness; (c), (g) Harmonic Centrality; and (d), (h) Eigenvector Centrality.
Four centrality metrics were computed within communities identified by both GMM and Infomap, and subsequently compared between awardees and other mathematicians. The metrics assessed were: (a), (e) Betweenness; (b), (f) Closeness; (c), (g) Harmonic Centrality; and (d), (h) Eigenvector Centrality.

Figure 4.

Distributed characteristics of mathematicians and mathematical awardees within communities.
Distributed characteristics of mathematicians and mathematical awardees within communities.

Algorithm 1

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Figure A1.

Communities and Sub-communities detected sequentially by GMM. The left sub-figure represents the result of the first detection on the collaboration network. The middle one is the community detected with most awardees in the first detection. The right one is network structure of one community in the second detection. The huge circle represents awardees, and the color indicates the sub-field of mathematicians.
Communities and Sub-communities detected sequentially by GMM. The left sub-figure represents the result of the first detection on the collaboration network. The middle one is the community detected with most awardees in the first detection. The right one is network structure of one community in the second detection. The huge circle represents awardees, and the color indicates the sub-field of mathematicians.

Algorithm 2

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Linear regression analysis on the number of awardees_

Algorithm #awardees
GMM Infomap
Community size 0.0056*** 0.0092***
Simpson index -0.1075* -0.0339***

The basic characteristics of mathematicians’ collaborative networks_

N L 〈k〉 lnN 〈C〉 density
79,016 342,022 8.657 11.2774 0.1972 0.0001

NMI analysis between true field labels and detected community labels_

Method GMM Infomap
Real NMI 0.2222 0.2404
Random NMI (0.03361, 0.03365) (0.08247, 0.08250)

The t-test of the difference of centrality metrics between awardees and other mathematicians_

Betweenness Closeness Harmonic centrality Eigenvector centrality
GMM 47,777.2381*** 0.0141*** 0.0245*** -0.0455***
Infomap 96.5236*** 0.0053 0.0323*** 0.1148***
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