In a range of scientific coauthorship networks, transitions emerge in degree distribution, in the correlation between degree and local clustering coefficient, etc. The existence of those transitions could be regarded because of the diversity in collaboration behaviors of scientific fields. A growing geometric hypergraph built on a cluster of concentric circles is proposed to model two specific collaboration behaviors, namely the behaviors of research team leaders and those of the other team members. The model successfully predicts the transitions, as well as many common features of coauthorship networks. Particularly, it realizes a process of deriving the complex “scale‐free” property from the simple “yes/no” decisions. Moreover, it provides a reasonable explanation for the emergence of transitions with the difference of collaboration behaviors between leaders and other members. The difference emerges in the evolution of research teams, which synthetically addresses several specific factors of generating collaborations, namely the communications between research teams, academic impacts and homophily of authors.
Citation between papers can be treated as a causal relationship. In addition, some citation networks have a number of similarities to the causal networks in network cosmology, e.g., the similar in-and out-degree distributions. Hence, it is possible to model the citation network using network cosmology. The casual network models built on homogenous spacetimes have some restrictions when describing some phenomena in citation networks, e.g., the hot papers receive more citations than other simultaneously published papers. We propose an inhomogenous causal network model to model the citation network, the connection mechanism of which well expresses some features of citation. The node growth trend and degree distributions of the generated networks also fit those of some citation networks well.
The increasing use of mathematical techniques in scientific research leads to the interdisciplinarity of applied mathematics. This viewpoint is validated quantitatively here by statistical and network analysis on the corpus PNAS 1999–2013. A network describing the interdisciplinary relationships between disciplines in a panoramic view is built based on the corpus. Specific network indicators show the hub role of applied mathematics in interdisciplinary research. The statistical analysis on the corpus content finds that algorithms, a primary topic of applied mathematics, positively correlates, increasingly co-occurs, and has an equilibrium relationship in the long-run with certain typical research paradigms and methodologies. The finding can be understood as an intrinsic cause of the interdisciplinarity of applied mathematics.
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