Social, technological, and biological systems are often represented as a complex network, whose structure reveals important properties of the system and leads to insights about its behavior. Many methods have been proposed over the past several decades to analyze the structure of complex networks, for example, to identify influential people in a social network or functional modules in a protein-protein interaction network. Most of these methods examine connections between entities only, and ignore interactions between them. In recent years, however, it has been recognized that network structure is the product of both its connections (i.e., topology) and the interactions taking place between entities in the network. These interactions determine how ideas, signals, pathogens, or influence flow along the connections, and different interactions may lead to different views of network structure.
This research project will lay the foundation for understanding the interplay between network structure, topology and dynamical interactions. It will develop a mathematical framework for interactions-aware network analysis that will lead to principled metrics and algorithms for finding communities or modules, measuring proximity between entities in a network, and distance between networks. Theoretical findings will be empirically validated using real-world network data on tasks such as identifying modules, predicting missing links and others. This new framework for network analysis will translate into new discoveries in computer science, sociology, biology and medicine.
