Related papers: A framework for cascade size calculations on rando…
How big is the risk that a few initial failures of nodes in a network amplify to large cascades that span a substantial share of all nodes? Predicting the final cascade size is critical to ensure the functioning of a system as a whole. Yet,…
Cascades on random networks are typically analyzed by assuming they map onto percolation processes and then are solved using generating function formulations. This approach assumes that the network is infinite and weakly connected, yet…
We introduce a probabilistic framework that represents stylized banking networks with the aim of predicting the size of contagion events. Most previous work on random financial networks assumes independent connections between banks, whereas…
We present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of random networks with arbitrary degree distribution and nonzero clustering introduced in [M.E.J. Newman, Phys.…
A probabilistic framework is introduced that represents stylized banking networks and aims to predict the size of contagion events. In contrast to previous work on random financial networks, which assumes independent connections between…
Cascade models are central to understanding, predicting, and controlling epidemic spreading and information propagation. Related optimization, including influence maximization, model parameter inference, or the development of vaccination…
How big is the risk that a few initial failures of networked nodes amplify to large cascades that endanger the functioning of the system? Common answers refer to the average final cascade size. Two analytic approaches allow its computation:…
We derive an exact expression for the probability density function of the cascade size (total progeny) in a continuous state branching process when the generations are Gamma distributed. The distribution has application in the modelling of…
Message-passing methods provide a powerful approach for calculating the expected size of cascades either on random networks (e.g., drawn from a configuration-model ensemble or its generalizations) asymptotically as the number $N$ of nodes…
The dynamics of diffusion in complex networks are widely studied to understand how entities, such as information, diseases, or behaviors, spread in an interconnected environment. Complex networks often present community structure, and tools…
Information spreads across social and technological networks, but often the network structures are hidden from us and we only observe the traces left by the diffusion processes, called cascades. Can we recover the hidden network structures…
The problem of cascading failures in cyber-physical systems is drawing much attention in lieu of different network models for a diverse range of applications. While many analytic results have been reported for the case of large networks,…
This paper considers a model for cascades on random networks in which the cascade propagation at any node depends on the load at the failed neighbor, the degree of the neighbor as well as the load at that node. Each node in the network…
We study the coevolutionary dynamics of network topology and social complex contagion using a threshold cascade model. Our coevolving threshold model incorporates two mechanisms: the threshold mechanism for the spreading of a minority state…
Two node variables determine the evolution of cascades in random networks: a node's degree and threshold. Correlations between both fundamentally change the robustness of a network, yet, they are disregarded in standard analytic methods as…
Cascades are ubiquitous in various network environments. How to predict these cascades is highly nontrivial in several vital applications, such as viral marketing, epidemic prevention and traffic management. Most previous works mainly focus…
We introduce a general framework for models of cascade and contagion processes on networks, to identify their commonalities and differences. In particular, models of social and financial cascades, as well as the fiber bundle model, the…
Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes…
Large but rare cascades triggered by small initial shocks are present in most of the infrastructure networks. Here we present a simple model for cascading failures based on the dynamical redistribution of the flow on the network. We show…
In a network, a local disturbance can propagate and eventually cause a substantial part of the system to fail, in cascade events that are easy to conceptualize but extraordinarily difficult to predict. Here, we develop a statistical…