  Modern scientific work, including writing papers and submitting research
grant proposals, increasingly involves researchers from different institutions.
In grant collaborations, it is known that institutions involved in many
collaborations tend to densely collaborate with each other, forming rich clubs.
Here we investigate higher-order rich-club phenomena in collaborative research
grants among institutions and their associations with research productivity.
Using publicly available data from the National Science Foundation in the US,
we construct a bipartite network of institutions and collaborative grants,
which distinguishes among the collaboration with different numbers of
institutions. By extending the concept and algorithms of the rich club for
dyadic networks to the case of bipartite networks, we find rich clubs both in
the entire bipartite network and the bipartite subnetwork induced by the
collaborative grants involving a given number of institutions up to five. We
also find that the collaborative grants within rich clubs tend to be more
productive in a per-dollar sense than the control. Our results highlight
advantages of collaborative grants among the institutions in the rich clubs.
