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Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
The rigidity of elastic networks depends sensitively on their internal connectivity and the nature of the interactions between constituents. Particles interacting via central forces undergo a zero-temperature rigidity-percolation transition…
Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…
In an increasingly connected world, the resilience of networked dynamical systems is important in the fields of ecology, economics, critical infrastructures, and organizational behaviour. Whilst we understand small-scale resilience well,…
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,…
Empirical complex systems must differentially respond to external perturbations and, at the same time, internally distribute information to coordinate their components. While networked backbones help with the latter, they limit the…
One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and…
From social interactions to the human brain, higher-order networks are key to describe the underlying network geometry and topology of many complex systems. While it is well known that network structure strongly affects its function, the…
This work targets the influence of disorder on the relaxed structure and macroscopic mechanical properties of elastic networks. We construct network classes of different types of disorder (length, topology and stiffness), which are…
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
Turing's theory of pattern formation is a universal model for self-organization, applicable to many systems in physics, chemistry and biology. Essential properties of a Turing system, such as the conditions for the existence of patterns and…
Prestrained elastic networks arise in a number of biological and technological systems ranging from the cytoskeleton of cells to tensegrity structures. To understand the response of such a network as a function of the prestrain, we consider…
In a sensor network, in practice, the communication among sensors is subject to:(1) errors or failures at random times; (3) costs; and(2) constraints since sensors and networks operate under scarce resources, such as power, data rate, or…
Natural systems are remarkably robust and resilient, maintaining essential functions despite variability, uncertainty, and hostile conditions. Understanding these nonlinear, dynamic behaviours is challenging because such systems involve…
Typically, contagion strength is modeled by a transmission rate $\lambda$, whereby all nodes in a network are treated uniformly in a mean-field approximation. However, local agents react differently to the same contagion based on their…
Spreading on networks is influenced by a number of factors including different parts of the inter-event time distribution (IETD), the topology of the network and non-stationarity. In order to understand the role of these factors we study…
A central concern of network operators is to estimate the probability of an incident that affects a significant part and thus may yield to a breakdown. We answer this question by modeling how a failure of either a node or an edge will…
Complex network theory has recently been proposed as a promising tool for characterising interactions between aircraft, and their downstream effects. We here explore the problem of networks' topological predictability, i.e. the dependence…