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In this work, we study the topological transition on the associated networks in a model proposed by Saeedian et al. (Scientific Reports 2019 9:9726), which considers a coupled dynamics of node and link states. Our goal was to better…
Many real world networks are characterized by adaptive changes in their topology depending on the dynamic state of their nodes. Here we study epidemic dynamics in an adaptive network, where susceptibles are able to avoid contact with…
Many-body systems when continuous phase transition occurs are mainly built in the interrelationship between particles, implemented through many-body correlations. Some of them may exhibit so-called topological order hardly measured by…
This paper addresses the problem of identifying the graph structure of a dynamical network using measured input/output data. This problem is known as topology identification and has received considerable attention in recent literature. Most…
The theory of pattern formation in reaction-diffusion systems is extended to the case of a directed network. Due to the structure of the network Laplacian of the scrutinised system, the dispersion relation has both real and imaginary parts,…
We explore the robustness of complex networks against physical damage. We focus on spatially embedded network models and datasets where links are physical objects or physically transfer some quantity, which can be disrupted at any point…
Hierarchical networks are attracting a renewal interest for modelling the organization of a number of biological systems and for tackling the complexity of statistical mechanical models beyond mean-field limitations. Here we consider the…
The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using…
The dynamical properties and mechanical functions of amorphous materials are governed by their microscopic structures, particularly the elasticity of the interaction networks, which is generally complicated by structural heterogeneity. This…
Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…
Complex network topologies and hyperbolic geometry seem specularly connected, and one of the most fascinating and challenging problems of recent complex network theory is to map a given network to its hyperbolic space. The Popularity…
We show that memory can be encoded in a model amorphous solid subjected to athermal oscillatory shear deformations, and in an analogous spin model with disordered interactions, sharing the feature of a deformable energy landscape. When…
Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural…
Network science can offer fundamental insights into the structural and functional properties of complex systems. For example, it is widely known that neuronal circuits tend to organize into basic functional topological modules, called…
Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on…
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…
Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of…
Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the usual appearance of a giant component as observed for the…
We introduce models of generic rigidity percolation in two dimensions on hierarchical networks, and solve them exactly by means of a renormalization transformation. We then study how the possibility for the network to self organize in order…