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Research on the vulnerability of electric networks with a complex network approach has produced significant results in the last decade, especially for transmission networks. These studies have shown that there are causal relations between…
In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a…
Previous research claimed or disclaimed the role of a small diameter in the synchronization of a network of coupled dynamical systems. We investigate this connection and show that it is two folds. We first construct two classes of networks,…
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
The transport on top of a periodic two-dimensional hexagonal magnetic pattern of (i) a single macroscopic steel sphere, (ii) a doublet of wax/magnetite composite spheres, and (iii) an immiscible mixture of ferrofluid droplets with a…
Although capillary and permeability are the two most important physical properties controlling fluid distribution and flow in nature, the interconnectivity function between them was a pressing challenge. Because knowing permeability leads…
Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the…
Predicting the macroscopic properties of thin fiber-based porous materials from their microscopic morphology remains challenging because of the structural heterogeneity of these materials. In this study, computational fluid dynamics…
We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which…
Understanding fluid movement in multi-pored materials is vital for energy security and physiology. For instance, shale (a geological material) and bone (a biological material) exhibit multiple pore networks. Double porosity/permeability…
Advances in imaging techniques enable high resolution 3D visualisation of vascular networks over time and reveal abnormal structural features such as twists and loops, and their quantification is an active area of research. Here we showcase…
Inspired by the structure of technological networks, we discuss network evolution mechanisms which give rise to topological properties found in real spatial networks. Thus, the peculiar structure of transport and distribution networks is…
This article analyzes the complex geometry of urban transportation networks as a gateway to understanding their encompassing urban systems. Using a proposed ring-buffer approach and applying it to 50 urban areas in the United States, we…
Many complex networks are only a part of larger systems, where a number of coexisting topologies interact and depend on each other. We introduce a layered model to facilitate the description and analysis of such systems. As an example of…
We explore the relation between the topological relevance of a node in a complex network and the individual dynamics it exhibits. When the system is weakly coupled, the effect of the coupling strength against the dynamical complexity of the…
Coherent transport promises to be the basis for an emerging new technology. Notwithstanding, a mechanistic understanding of the fundamental principles behind optimal scattering media is still missing. Here, complex network analysis is…
Digital topology has its own working conditions and sometimes differs from the normal topology. In the area of topological robotics, we have important counterexamples in this study to emphasize this red line between a digital image and a…
Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of…
A method of modelling the three-dimensional microstructure of random isotropic two-phase materials is proposed. The information required to implement the technique can be obtained from two-dimensional images of the microstructure. The…
Most real-world complex systems can be modelled by coupled networks with multiple layers. How and to what extent the pattern of couplings between network layers may influence the interlaced structure and function of coupled networks are not…