Complex network research is not a single discipline — it is highly interdisciplinary, seeking the answers to some fundamental questions about living, adaptable, and changeable systems. Several of the main disciplines are “network theory” involving the research areas of computer science, networks science, and graph theory. Another is “network science (NS)” attempting to research engineered networks, information networks, biological networks, semantic networks, and social networks while “dynamic network analysis (DNA)” will use traditional social network analysis, link analysis and multi-agent systems involving large amounts of electronic data. We should also add “complex adaptive systems” that is grounded in modern chemistry, biological views on adaption, expatriation, and evolution. In all of these and more network related areas the study of emergence and self-organization are fundamental. Although academic disciplines are hugely diverse in complex network research, here in the Department of Physics, disciplines in statistical analysis involving physics, mathematics, and computational analysis (data mining) are its primary focus.
Professor László Barabási is Director of the Center for Complex Network Research which currently focuses on two main lines of research: systems biology and social networks. Our research on systems biology focuses on the properties of biological networks, with applications to metabolic modeling, flux balance methods, and human diseases. The research on social networks involves the study and modeling of extensive communication datasets.
Recently Professor Alessandro Vespignani’s research activity focuses on the interdisciplinary application of statistical and numerical simulation methods in the analysis of epidemic and spreading phenomena and the study of biological, social and technological networks. For several years he has been working on the characterization and modeling of the Internet, the WWW and large-scale information networks. He is now focusing his research activity in modeling the spatial spread of epidemics, including the realistic and data-driven computational modeling of emerging infectious diseases, the resilience of complex networks and the behavior of techno-social systems.
Professor Dmitri Krioukov’s research mainly focuses on theoretical and mathematical aspects of network science. He develops and applies methods in non-Euclidean geometry and theoretical physics to the analysis of complex networks. Non-Euclidean geometry of complex networks explains their structure, predicts their dynamics, and enables maximally efficient and robust navigation on these networks.
Professor Krioukov and his collaborators have recently shown that the network representing the global structure of our universe has asymptotically the same structure and dynamics as many real networks in nature and society. The growth rules of the universe and the Internet, or even the brain, are asymptotically identical. These results suggest that the canonical approach in theoretical physics may be applicable to networks. If true, this hypothesis may help to predict and control network dynamics. The lack of fundamental theory of this dynamics is one of many factors making the network prediction and control tasks extremely challenging in many practically relevant applications. Some other focus areas of Professor Krioukov’s current/recent research include brain networks, mathematical connections between different ensembles of random graphs, and certain networks in pure mathematics, such as networks of numbers and Apollonian sphere packings.