A number of real-world networks are, in fact, one-mode projections of bipartite networks comprised of two types of nodes. For institutions engaging in collaboration for technological innovation, the underlying network is bipartite with institutions (agents) linked to the patents they have filed (artifacts), while the projection is the co-patenting network. Projected network topology is highly affected by the underlying bipartite structure, hence a lack of understanding of the bipartite network has consequences for the information that might be drawn from the one-mode co-patenting network. Here, we create an empirical bipartite network using data from 2.7 million patents. We project this network onto the agents (institutions) and look at properties of both the bipartite and projected networks that may play a role in knowledge sharing and collaboration. We compare these empirical properties to those of synthetic bipartite networks and their projections in order to understand the processes that might operate in the network formation. A good understanding of the topology is critical for investigating the potential flow of technological knowledge. We show how degree distributions and small cycles affect the topology of the one-mode projected network - specifically degree and clustering distributions, and assortativity. We propose new network-based metrics to quantify how collaborative agents are in the co-patenting network. We find that several large corporations that are the most collaborative agents in the network, however such organisations tend to have a low diversity of collaborators. In contrast, the most prolific institutions tend to collaborate relatively little but with a diverse set of collaborators. This indicates that they concentrate the knowledge of their core technical research, while seeking specific complementary knowledge via collaboration with smaller companies.