Related papers: Disentangling shock diffusion on complex networks:…
An important challenge in several disciplines is to understand how sudden changes can propagate among coupled systems. Examples include the synchronization of business cycles, population collapse in patchy ecosystems, markets shifting to a…
Measuring and optimizing the influence of nodes in big-data online social networks are important for many practical applications, such as the viral marketing and the adoption of new products. As the viral spreading on social network is a…
In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…
Cascading failures are a critical vulnerability of complex information or infrastructure networks. Here we investigate the properties of load-based cascading failures in real and synthetic spatially-embedded network structures, and propose…
Understanding propagation structures in graph diffusion processes, such as epidemic spread or misinformation diffusion, is a fundamental yet challenging problem. While existing methods primarily focus on source localization, they cannot…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
Following the financial crisis of 2007-2008, a deep analogy between the origins of instability in financial systems and complex ecosystems has been pointed out: in both cases, topological features of network structures influence how easily…
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…
In many complex networked systems, such as online social networks, activity originates at certain nodes and subsequently spreads on the network through influence. In this work, we consider the problem of modeling the spread of influence and…
When a plane shock hits a wedge head on, it experiences a reflection-diffraction process and then a self-similar reflected shock moves outward as the original shock moves forward in time. Experimental, computational, and asymptotic analysis…
We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the…
A simple banking network model is proposed which features multiple waves of bank defaults and is analytically solvable in the limiting case of an infinitely large homogeneous network. The model is a collection of nodes representing…
There is empirical evidence from a range of disciplines that as the connectivity of a network increases, we observe an increase in the average fitness of the system. But at the same time, there is an increase in the proportion of…
A crucial challenge in network theory is the study of the robustness of a network after facing a sequence of failures. In this work, we propose a dynamical definition of network's robustness based on Information Theory, that considers…
We study the distributions of the resilience of power flow models against transmission line failures via a so-called backup capacity. We consider three ensembles of random networks and in addition, the topology of the British transmission…
In this paper we study a simple cascading process in a structured heterogeneous population, namely, a network composed of two loosely coupled communities. We demonstrate that under certain conditions the cascading dynamics in such a network…
We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the…
Information diffusion and virus propagation are fundamental processes taking place in networks. While it is often possible to directly observe when nodes become infected with a virus or adopt the information, observing individual…
Climate change is reshaping species interactions and movement across fragmented landscapes. Despite this, most mathematical models assume random diffusion, overlooking the influence of directed movement. Here, we develop a graph based…
Stabilizing large networks of nonlinear agents is challenging; decomposition and distributed analysis of these networks are crucial for computational tractability and information security. Vidyasagar's Network Dissipativity Theorem enables…