Random Walks on Modular Networks
With the increasing power of high throughput technologies and storage capacities, more and more datasets from real-world systems in the form of complex networks become available. Similarly, also the area of network analysis has expanded rapidly and attracted a lot of attention over the last 10 years. Networks are now widely recognized not only as outcomes of complex interactions, but as key determinants of structure, function, and dynamics in systems that span the biological, physical, and social sciences. The so called “new science of networks” has introduced novel paradigms of basic system properties, such as scale-free networks, small-world properties, and the importance of motifs and/or organization into modules, and of hub states.
During the last years, new strategies have been developed for studying complex networks. Particularly, the method of random walks, as has been well-established for global analysis of networks, can fully account for local as well as global topological structure within the network and proved to be very useful for finding modules and hubs in modular networks. Our project aims at developing rigorous statements about optimal module and hub state identification and at designing efficient algorithms for that purpose.
The project is funded through the Berlin Mathematical School (BMS) and the International Max Planck Research School “Computational Biology and Scientific Computing”.
- Sarich, M. and Schuette, Ch. and Vanden-Eijnden, E. (2010) Optimal Fuzzy Aggregation of Networks. Multiscale Modeling and Simulation, 8 (4). pp. 1535-1561.
- Djurdjevac, N. and Sarich, M. and Schuette, Ch. (2010) On Markov State Models for Metastable Processes. In: Proceedings of ICM 2010, Invited Talks.