A layered framework to study collaboration as a form of knowledge sharing and diffusion

Collaboration can be described using layered systems such as the article–author–institute–country structure. These structures can be considered ‘cascades’ or ‘chains’ of bipartite networks. We introduce a framework for characterizing and studying the intensity of collaboration between entities at a given level (e.g., between institutions). Specifically, we define the notions of significant, essential and vital nodes, and significant, essential and vital sub paths to describe the spread of knowledge through collaboration in such systems. Based on these notions, we introduce relative and absolute proper essential node (PEN) centrality as indicators of a node's importance for diffusion of knowledge through collaboration.