From brain to earth and climate systems: Small-world interaction networks or not?

We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with commonly used time series analysis based approaches to network characterization

Quantifying long-range correlations in complex networks beyond nearest neighbors

We propose a fluctuation analysis to quantify spatial correlations in complex networks. The approach considers the sequences of degrees along shortest paths in the networks and quantifies the fluctuations in analogy to time series. In this work, the Barabasi-Albert (BA) model, the Cayley tree at the percolation transition, a fractal network model, and examples of real-world networks are studied. While the fluctuation functions for the BA model show exponential decay, in the case of the Cayley tree and the fractal network model the fluctuation functions display a power-law behavior. The fractal network model comprises long-range anti-correlations. The results suggest that the fluctuation exponent provides complementary information to the fractal dimension

Analysis and minimization of bending losses in discrete quantum networks

We study theoretically the transfer of quantum information along bends in two-dimensional discrete lattices. Our analysis shows that the fidelity of the transfer decreases considerably, as a result of interactions in the neighbourhood of the bend. It is also demonstrated that such losses can be controlled efficiently by the inclusion of a defect. The present results are of relevance to various physical implementations of quantum networks, where geometric imperfections with finite spatial extent may arise as a result of bending, residual stress, etc

The effects of spatial constraints on the evolution of weighted complex networks

Motivated by the empirical analysis of the air transportation system, we define a network model that includes geographical attributes along with topological and weight (traffic) properties. The introduction of geographical attributes is made by constraining the network in real space. Interestingly, the inclusion of geometrical features induces non-trivial correlations between the weights, the connectivity pattern and the actual spatial distances of vertices. The model also recovers the emergence of anomalous fluctuations in the betweenness-degree correlation function as first observed by Guimer\`a and Amaral [Eur. Phys. J. B {\bf 38}, 381 (2004)]. The presented results suggest that the interplay between weight dynamics and spatial constraints is a key ingredient in order to understand the formation of real-world weighted networks

Hydrological controls on river network connectivity

This study proposes a probabilistic approach for the quantitative assessment of reach- and network-scale hydrological connectivity as dictated by river flow space–time variability. Spatial dynamics of daily streamflows are estimated based on climatic and morphological features of the contributing catchment, integrating a physically based approach that accounts for the stochasticity of rainfall with a water balance framework and a geomorphic recession flow analysis. Ecologically meaningful minimum stage thresholds are used to evaluate the connectivity of individual stream reaches, and other relevant network-scale connectivity metrics. The framework allows a quantitative description of the main hydrological causes and the ecological consequences of water depth dynamics experienced by river networks. The analysis shows that the spatial variability of local-scale hydrological connectivity is strongly affected by the spatial and temporal distribution of climatic variables. Depending on the underlying climatic settings and the critical stage threshold, loss of connectivity can be observed in the headwaters or along the main channel, thereby originating a fragmented river network. The proposed approach provides important clues for understanding the effect of climate on the ecological function of river corridors

On the Spatial Pattern of Input-Output Metrics for a Network Synchronization Process

A graph-theoretic analysis is undertaken for a compendium of input-output (transfer) metrics of a standard discrete-time linear synchronization model, including lp gains, frequency responses, frequency-band energy, and Markov parameters. We show that these transfer metrics exhibit a spatial degradation, such that they are monotonically nonincreasing along vertex cutsets away from an exogenous input. We use this spatial analysis to characterize signal-to-noise ratios (SNRs) in diffusive networks driven by process noise, and to develop a notion of propagation stability for dynamical networks. Finally, the formal results are illustrated through an example