Djurdjevac, Nataša
[Author]
;
djurdjev@mi.fu-berlin.de
[Contributor];
w
[Contributor];
Christof Schütte
[Contributor];
Wilhelm Huisinga
[Contributor]
Methods for analyzing complex networks using random walker approaches ; Neue Methoden zur Analyse von komplexen Netzwerken mittels Zufallsspaziergängen
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Media type:
Doctoral Thesis;
Electronic Thesis;
E-Book
Title:
Methods for analyzing complex networks using random walker approaches ; Neue Methoden zur Analyse von komplexen Netzwerken mittels Zufallsspaziergängen
Contributor:
Djurdjevac, Nataša
[Author]
Published:
Freie Universität Berlin: Refubium (FU Berlin), 2012
Footnote:
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Description:
Real-world systems are often modeled as networks. Many algorithms for analyzing such complex networks are oriented towards finding modules that are densely inter-connected substructures having sparse connections to the rest of the network, and finding hub nodes that are key connectors of modules. In many cases these modules and hubs correspond to relevant structures in the original system. For example in biological systems, modules often correspond to functional units and hubs to essential parts of this system. In this thesis we developed a new mathematical framework that can be effectively applied for analyzing complex networks. This framework is based on defining a new type of random walk processes on networks and using spectral methods for finding modules and hubs. When considering random walk processes on networks, modules represent metastable sets of this process. There are two crucial differences in the approach presented in this thesis compared to standard random-walk- based methods for module finding. Firstly, we have defined a new time- continuous random walk process characterized by waiting times in each node which results in increased metastability of the process in densely connected areas of the network-modules. In this way we have overcome the problem of most standard random walk processes for which also nonmodular structures (for example long chains) represent metastable sets. The second difference results from the fact that most of the state-of-the-art approaches for module finding focus on finding a full partition of a network. The method introduced in this thesis finds a fuzzy decomposition of a network into modules, where nodes can be assigned to more than one module with a certain probability. In order to find such modules we used Markov State Models (MSM) as low-dimensional models for metastable Markov processes. We generalized the standard MSM approach that is based on full partitioning of the state space and developed a fuzzy MSM, where nodes that are assigned to some module with ...