Modeling and analyzing empirical systems by using the concepts of complex networks

Network construction is an acceptable approach for better understanding the behavior of complex system which can be used to reveal the pattern of collective dynamics for realizing physical interactions in the dynamical system. In this case, characterizing functional connectivity of complex networks for studying a broad class of natural and artificial systems from the measures of correlation and causality is of utmost importance to correctly unravel physical phenomena of the system. Many network reconstruction approaches are based on heuristically thresholding the correlation matrices resulting from pairwise correlation analysis according to experimental methods. Other approaches compare the observed correlations against null models in the statistical analyses, obtaining results which are statistically robust. Different methods were used, including cross-correlation (CC), spectral coherence (SpeCoh), mutual information (MI), transfer entropy (TE), Spearman's rank correlation (SC) and convergent cross-mapping (CCM). The methods were applied to linear and nonlinear collective dynamics by autoregressive moving average (ARMA) and Logistic map (LOG) models, respectively. The dynamics of interconnected units was simulated from different complex topologies widely observed in empirical systems with well-known network models. The methods of MI and CCM were chosen after examining on the artificial cases consisting of desirable features of the real systems. The results show that network reconstruction dramatically depends on the interplay between the (unknown) underlying structure and the (unknown) underlying dynamics and high values of the area under curve of receiver operating characteristic around 72% obtain for the selected network topologies.