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Cascading failures in complex systems have been studied extensively using two different models: $k$-core percolation and interdependent networks. We combine the two models into a general model, solve it analytically and validate our…
Spectral inference on multiple networks is a rapidly-developing subfield of graph statistics. Recent work has demonstrated that joint, or simultaneous, spectral embedding of multiple independent networks can deliver more accurate estimation…
Recently, the percolation transition has been characterized on interacting networks both in presence of interdependent and antagonistic interactions. Here we characterize the phase diagram of the percolation transition in two Poisson…
For ordinary (independent) percolation on a large class of lattices it is well known that below the critical percolation parameter $p_c$ the cluster size distribution has exponential decay and that power-law behavior of this distribution…
This Letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erd\"{o}s and R\'{e}nyi (ER) random network. The class of the percolation is implemented by introducing a best-of-m rule. Two…
We study scale-free networks constructed via a cooperative Achlioptas growth process. Links between nodes are introduced in the network in order to produce a scale-free graph with given exponent lambda for the degree distribution, but the…
The recent proliferation of correlated percolation models---models where the addition of edges/vertices is no longer independent of other edges/vertices---has been motivated by the quest to find discontinuous percolation transitions. The…
The ability to navigate light signals in two-dimensional networks of waveguide arrays is a prerequisite for the development of all-optical integrated circuits for information processing and networking. In this article, we present a…
In this work, we propose an interdependent, multilayer network model and percolation process that matches infrastructures better than previous models by allowing some nodes to survive when their interdependent neighbors fail. We consider a…
Communication networks, power grids, and transportation networks are all examples of networks whose performance depends on reliable connectivity of their underlying network components even in the presence of usual network dynamics due to…
A model of interdependent networks of networks (NoN) has been introduced recently in the context of brain activation to identify the neural collective influencers in the brain NoN. Here we develop a new approach to derive an exact…
In reality, many real-world networks interact with and depend on other networks. We develop an analytical framework for studying interacting networks and present an exact percolation law for a network of $n$ interdependent networks (NON).…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
We study the spreading of two mutually cooperative diseases on different network topologies, and with two microscopic realizations, both of which are stochastic versions of an SIR type model studied by us recently in mean field…
k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understand the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with…
We study a model for a statistical network formed by interactions between its nodes and links. Each node can be in one of two states (Ising spin up or down) and the node-link interaction facilitates linking between the like nodes. For high…
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…
We study a problem of failure of two interdependent networks in the case of correlated degrees of mutually dependent nodes. We assume that both networks (A and B) have the same number of nodes $N$ connected by the bidirectional dependency…
Understanding the resilience of infrastructures such as transportation network has significant importance for our daily life. Recently, a homogeneous spatial network model was developed for studying spatial embedded networks with…
The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong…