Networks/Theory V

Networks constitute a paradigm of complexity in real life systems by assembling the structure of the interactions of their elementary constituents [2, 3]. They are found at every level of biological organisation, from genes inside the cells to the trophic relations between species in large ecosys- tems [3]. Nowadays, with the enormous development of data science, there is a huge interest re- lated to the network inference, namely detecting the interacting structure from external measure- ments or observations.

A large number of complex systems, naturally emerging in various domains, are well described by directed networks, resulting in numerous interesting features that are absent from their undirected counterparts. Among these properties is a strong non-normality, inherited by a strong asymmetry, which stands out as a universal signature that characterizes such systems and guides their underlying hierarchy. In this talk, we consider an extensive collection of empirical networks and analyze their structural properties by using tools such as the entropy rate borrowed from information theory.

Many real-world complex systems have small-world topology characterized by the high clustering of nodes and short path lengths. It is well-known that higher clustering drives localization while shorter path length supports delocalization of the eigenvectors of networks. Using multifractals technique, we investigate localization properties of the eigenvectors of the adjacency matrices of small-world networks constructed using Watts-Strogatz algorithm.

The detection of causal interactions between variables is of great importance when inferring complex networks but also remains challenging due to the high-dimensionality and nonlinearity of observational time series with a limited sample size. Convergent cross mapping (CCM) based on nonlinear state space reconstruction, as a network inference model, made substantial progress by measuring how well historical values of one variable can reliably estimate states of other variables.