"Success" of firms in venture capital markets is hard to define, and its determinants are still poorly understood. We build a bipartite network of investors and firms in the healthcare sector, describing its structure and its communities. Then, we characterize "success" introducing progressively more refined definitions, and we find a positive association between such definitions and the centrality of a company. In particular, we are able to cluster funding trajectories of firms into two groups capturing different "success" regimes and to link the probability of belonging to one or the other to their network features (in particular their centrality and the one of their investors). We further investigate this positive association by introducing scalar as well as functional "success" outcomes, confirming our findings and their robustness.