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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.

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Discovering and constructing the topological structure in data has attracted the attention within the community of data analysis. However, most methods developed so far are unsuitable for very large sets of data because of their computational difficulties. This paper presents a fast algorithm for constructing the inherent topological structure in large sets of data that might be noisy in order to enhance the MAPPER algorithm introduced by Singh, Mémoli and Carlsson. The limitation of our method, as shown by our experiments, lies with the storage in the main memory rather than the computing time.