Community structure in real-world networks from a non-parametrical synchronization-based dynamical approach

[EN]This work analyzes the problem of community structure in real-world networks based on the synchronization of nonidentical coupled chaotic Rössler oscillators each one characterized by a defined natural frequency, and coupled according to a predefined network topology. The interaction scheme contemplates an uniformly increasing coupling force to simulate a society in which the association between the agents grows in time. To enhance the stability of the correlated states that could emerge from the synchronization process, we propose a parameterless mechanism that adapts the characteristic frequencies of coupled oscillators according to a dynamic connectivity matrix deduced from correlated data. We show that the characteristic frequency vector that results from the adaptation mechanism reveals the underlying community structure present in the network.

Communities in complex networks

The study of complex networks has attracted the attention of the scientific community for many obvious reasons. A vast number of systems, from the brain to ecosystems, power grid, and the Internet, can be represented as large complex networks, i.e, assemblies of many interacting components with nontrivial topological properties. The link between these components can describe a global behaviour such as the Internet traffic, electricity supply service, market trend, etc. One of the most relevant topological feature of graphs representing these complex systems is community structure which aims to identify the modules and, possibly, their hierarchical organization, by only using the information encoded in the graph topology. Deciphering network community structure is not only important in order to characterize the graph topologically, but gives some information both on the formation of the network and on its functionality.