  In this paper, we present a method to project co-authorship networks, that
accounts in detail for the geometrical structure of scientists collaborations.
By restricting the scope to 3-body interactions, we focus on the number of
triangles in the system, and show the importance of multi-scientists (more than
2) collaborations in the social network. This motivates the introduction of
generalized networks, where basic connections are not binary, but involve
arbitrary number of components. We focus on the 3-body case, and study
numerically the percolation transition.
