A distributed hypergraph model for simulating the evolution of large coauthorship networks

Abstract

The coauthorship in a paper set can be expressed by a hypergraph, namely a system with heterogeneously multinary relationship. The coauthorship network of that paper set is the simple graph extracted from that hypergraph. We designed a distributed hypergraph model to simulate the dynamics of large coauthorship networks in a full-scale manner. Its assembly mechanism of hyperedges is driven by Lotka’s law and a cooperative game that maximizes a benefit-cost ratio for coauthoring a paper. The model is built on a circle to express the game, expressing the cost by the distance between nodes. The benefit of coauthoring with a productive author or one with many coauthors is expressed by the cumulative degree or hyperdegree of nodes. The model successfully simulates the multimodal features emerged in the evolutions of coauthorship patterns, the clustering of nodes, the degree assortativity of linked nodes, degree and hyperdegree distributions. This model has the potential to be a null model for studying the complexity of the large social networks arising from other specific collaboration behaviors.

Appendix

We applied the model to simulate the coauthorship networks extracted from the papers of three accredited journals of informetrics, namely the Journal of the Association for Information Science and Technology, Journal of Informetrics, and Scientometrics. The dataset considered here, named “informetr” (Table 3), consists the papers published at the years from 1998 to 2019, where authors’ name is extracted from the term “AF” in the raw data downloaded from Web of Science². The papers at 1998–2021 are used to extract nodes’ historical degree and hyperdegree. The coauthorship network extracted from the papers at 2002–2019 will be simulated in full scale by our model. Notably, using the term “AF” suffers the splitting and merging errors on names. Simulating a dataset with errors helps to test the fault tolerance of our model.

Table 3 The information of the dataset informetr

Fig. 16 shows the fitting polynomial of the cumulative number of nodes and that of the annual number of hyperedges in synth-informetr. It indicates that the mathematical formulae underlying our model also hold for this dataset. The number of new nodes at each time step is proportional to the corresponding number of informetr, where the proportion $\varepsilon =7$. Six processes are used to run the model. When $\alpha =1.6$, $\beta =0.0007$, and $\gamma =0.8$, the model can generate hyperdegree and degree distributions with approximate shapes to those of informetr. When $\epsilon =0.0019$, the difference between the size of the giant component of informetr 2002–2019 and that of synth-informetr is smaller than 0.1.

Fig. 16

The increasing trend of synth-informetr. Panel a shows the cumulative number of nodes and its fitting polynomial $y(t)=\sum ^2_{l=0}a_lt^l$, where $a_0=-1.356$e+03, $a_1=1.423$e+03, and $a_2=1.642$e+02. Panel b shows that the annual number of hyperedges and its fitting polynomial $y(t)=\sum ^1_{l=0}b_lt^l$, where $b_0=1.641$e+2 and $b_1=3.219$e+01. Panel c shows the contributions of the leading terms to these polynomials

Table 4 shows certain statistical indexes of the coauthorship networks extracted from informetr and from synth-informetr. Figs. 17, 18, 19, 20, 21, 2223 and 24 show that the model can captures the coauthorship patterns in informetr, and can reproduce the evolutions of coauthorship patterns, the clustering of nodes, the degree assortativity, the degree distribution, and so on.

Table 4 Network indexes of informetr and synth-informetr

Fig. 17

Coauthoring patterns from the perspective of multinary relationship. The panels show the fractions of the patterns, defined in the caption of Fig. 9, of informetr (red bars) and those of synth-informetr (blue bars)

Fig. 18

Coauthoring patterns from the perspective of binary relationship. The panels show the fractions of the patterns, defined in the caption of Fig.10, of informetr (red bars) and those of synth-informetr (blue bars)

Fig. 19

The proportion of the authors who publish one paper. The $r_t$ is this proportion of informetr, and $r_s$ is that of the synth-informetr. The panels show this proportion for the authors in informetr who have the same number of coauthors (red squares) and that for synth-informetr (blue circles)

Fig. 20

The correlation between the number of papers and the number of coauthors. The panels show the average number of coauthors of the authors in informetr who have the same number of papers at [2002, y] (red circles) and that in synth-informetr (blue squares). The Spearman correlation coefficient, $r_t$, for informetr and that, $r_s$, for synth-informetr are significantly larger than 0, p-value $<0.05$

Fig. 21

The local clustering coefficient. The panels show the average of this value for the authors in informetr who have degree k at [2002, y] (red circles) and that for synth-informetr (blue circles)

Fig. 22

The average degree of coauthors. The panels show the average of this value for the authors in informetr who have degree k at [2002, y] (red circles) and that for synth-informetr (blue squares)

Fig. 23

The distribution of the number of an author’s papers. The panels show this distribution for informetr (red circles) and that for synth-informetr (blue squares)

Fig. 24

The distribution of the number of an author’s coauthors. The panels show the distribution for informetr (red circles) and that for synth-informetr (blue squares)