  Collaborations and citations within scientific research grow simultaneously
and interact dynamically. Modelling the coevolution between them helps to study
many phenomena that can be approached only through combining citation and
coauthorship data. A geometric graph for the coevolution is proposed, the
mechanism of which synthetically expresses the interactive impacts of authors
and papers in a geometrical way. The model is validated against a data set of
papers published on PNAS during 2007-2015. The validation shows the ability to
reproduce a range of features observed with citation and coauthorship data
combined and separately. Particularly, in the empirical distribution of
citations per author there exist two limits, in which the distribution appears
as a generalized Poisson and a power-law respectively. Our model successfully
reproduces the shape of the distribution, and provides an explanation for how
the shape emerges via the decisions of authors. The model also captures the
empirically positive correlations between the numbers of authors' papers,
citations and collaborators.
