April 03, 2013, ESB 2001

The properties of dynamical systems taking place on networks, such as opinion dynamics, synchronisation, consensus or random walks, are strongly related to the structure of the network. In particular every consensus dynamics provides a centrality measure of the nodes and edges in the network, and---through time scale separation---a way to cluster the nodes into communities, i.e. sets of densely connected nodes. This dynamical approach to large networks analysis highlights unexpected links between various notions such as PageRank, MinCut, modularity and spectral clustering. We illustrate our methods on social, biological (proteins) and technological (power networks, Internet) networks.

Jean-Charles Delvenne is assistant professor at University of Louvain (Belgium) since 2010, where here also graduated as a PhD in 2005. In the mean time, he spent time at University of Padua (Italy), Caltech (California), Imperial college London (UK), University of Namur (Belgium). He is interested in dynamical systems, control, and discrete mathematics. In particular, he studies statistical physics methods for control, and the interaction between structure and dynamics in large networks of interconnected systems.