Tie strength distribution in scientific collaboration networks

Science is increasingly dominated by teams. Understanding patterns of scientific collaboration and their impacts on the productivity and evolution of disciplines is crucial to understand scientific processes. Electronic bibliography offers a unique opportunity to map and investigate the nature of scientific collaboration. Recent studies have demonstrated a counterintuitive organizational pattern of scientific collaboration networks: densely interconnected local clusters consist of weak ties, whereas strong ties play the role of connecting different clusters. This pattern contrasts itself from many other types of networks where strong ties form communities while weak ties connect different communities. Although there are many models for collaboration networks, no model reproduces this pattern. In this paper, we present an evolution model of collaboration networks, which reproduces many properties of real-world collaboration networks, including the organization of tie strengths, skewed degree and weight distribution, high clustering, and assortative mixing.

Figure 1

The correlation between link overlap $O_{ij}$ and link weight $w_{ij}$ in scientific collaboration network of (a) network science, (b) high-energy physics, (c) astrophysics, and (d) condensed matter. We use logarithmic binning for $w_{ij}$. The error bars indicate the standard error of the mean $O_{ij}$. For a large portion of links, overlap decreases with weight. For a small portion of strongest links, overlap increases with weight.

Figure 2

The robustness of scientific collaboration network of (a) network science, (b) high-energy physics, (c) astrophysics, and (d) condensed matter under the removal of strong (weak) ties. The control parameter $f$ means the fraction of removed links. The removal of links is on the basis of their strength $w_{ij}$. The black dashed curves correspond to the removal of links from weak to strong. The red solid curves correspond to the removal of links from strong to weak. The relative size of largest connected component (LCC) $R_{\text{LCC}}=N_{\text{LCC}}/N$ indicates that the removal of strong links leads to a faster breakdown of networks.

Figure 3

Visualization of the structure of network science collaboration network and link removal process. (a) The whole network structure with 379 nodes and 914 links. The color of each node indicates its community membership obtained by Louvain method [39]. (b) The remaining subgraph after removal of $43\%$ strongest links. The shaded region indicates largest connected component. (c) The remaining subgraph after removal of $43\%$ weakest links.

Figure 4

Model results with different $\alpha$. Top: correlation between $O_{ij}$ and $w_{ij}$; Bottom: model network robustness to link removal. Left, $\alpha =0$; middle, $\alpha =1$; right, $\alpha =3$.

Figure 5

Our model produces skewed degree and weight distributions. Complementary cumulative (top) degree and (bottom) weight distributions. Left, $\alpha =0$; middle, $\alpha =1$; right, Hep-th.

Figure 6

Comparison of calculation results with numerical results of (a) number of of groups $n_g\left(t\right)$ and (b) number of students $n_s\left(t\right)$. The numerical results are averaged over 100 repetitions.

Figure 7

(Top) Weight-overlap correlation and (bottom) robustness to link removal when (left) $G=6$ and (right) $G=8$.

Figure 8

(Top) Weight-overlap correlation and (bottom) robustness to link removal when (left) $f=0.1$ and (right) $f=0.3$.