Field-Theoretical Approach to Complex Networks

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We propose to create new tools for describing complex network systems by extending and modifying techniques used in theoretical physics for the description of disordered mesoscopic systems. We intend to provide a framework for a universal description of stochastic propagation through complex network systems belonging to different classes. Taking into account both dynamical disorder (due to the inevitable stochasticity of the input) and quenched disorder (that models complex networks of different topologies), we will formulate a set of relevant Langevin equations defined on discrete manifolds (networks). To achieve the universal description, we are going to cast these equations into the form of an effective field theory. This would allow us first to classify the networks (crucially, allowing both for the character of random signal and / simultaneously / for the network topology) and thus present new universality classes that emerge as the result of this complexity, and then to use powerful field theoretical methods for determining and calculating relevant observable quantities on the complex network.