Sophisticated methods for analysing complex networks promise to be of great benefit to almost all scientific disciplines, yet they elude us. In this work, we make fundamental methodological advances to rectify this. We discover that the interaction between a small number of roles, played by nodes in a network, can characterize a network%s structure and also provide a clear real-world interpretation. Given this insight, we develop a framework for analysing and comparing networks, which outperforms all existing ones. We demonstrate its strength by uncovering novel relationships between seemingly unrelated networks, such as Facebook, metabolic, and protein structure networks. We also use it to track the dynamics of the world trade network, showing that a countrys role of a broker between non-trading countries indicates economic prosperity, whereas peripheral roles are associated with poverty. This result, though intuitive, has escaped all existing frameworks. Finally, our approach translates network topology into everyday language, bringing network analysis closer to domain scientists.
COBISS.SI-ID: 2048292371
Inferring the internal interaction patterns of a complex dynamical system is a challenging problem. Traditional methods often rely on examining the correlations among the dynamical units. However, in systems such as transcription networks, one unit's variable is also correlated with the rate of change of another unit's variable. Inspired by this, we introduce the concept of derivative-variable correlation, and use it to design a new method of reconstructing complex systems (networks) from dynamical time series. Using a tunable observable as a parameter, the reconstruction of any system with known interaction functions is formulated via a simple matrix equation. We suggest a procedure aimed at optimizing the reconstruction from the time series of length comparable to the characteristic dynamical time scale. Our method also provides a reliable precision estimate. We illustrate the method's implementation via elementary dynamical models, and demonstrate its robustness to both model error and observation error.
COBISS.SI-ID: 2048303635
The topology behind biological interaction networks has been studied for over a decade. Yet, there is no definite agreement on the theoretical models which best describe protein-protein interaction (PPI) networks. Such models are critical to quantifying the significance of any empirical observation regarding those networks. Here, we perform a comprehensive analysis of yeast PPI networks in order to gain insights into their topology and its dependency on interaction-screening technology. We find that: (1) interaction-detection technology has little effect on the topology of PPI networks; (2) topology of these interaction networks differs in organisms with different cellular complexity (human and yeast); (3) clear topological difference is present between PPI networks, their functional sub-modules, and their inter-functional “linkers”; (4) high confidence PPI networks have more “geometrical” topology compared to predicted, incomplete, or noisy PPI networks; and (5) inter-functional “linker” proteins serve as mediators in signal transduction, transport, regulation and organisational cellular processes.
COBISS.SI-ID: 2048314899