Related papers: Phase transitions in optimally robust network stru…
We consider a general model in which there is a coupled dynamics of node states and links states in a network. This coupled dynamics coevolves with dynamical changes of the topology of the network caused by a link rewiring mechanism. Such…
We study a network model that couples the dynamics of link states with the evolution of the network topology. The state of each link, either A or B, is updated according to the majority rule or zero-temperature Glauber dynamics, in which…
Robustness of network of networks (NON) has been studied only for dependency coupling (J.X. Gao et. al., Nature Physics, 2012) and only for connectivity coupling (E.A. Leicht and R.M. D Souza, arxiv:0907.0894). The case of network of n…
Multi-stability is a widely observed phenomenon in real complex networked systems, such as technological infrastructures, ecological systems, gene regulation, transportation and more. When a system functions normally but there exists also a…
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…
A temporal graph is a graph whose edges appear only at certain points in time. Recently, the second and the last three authors proposed a natural temporal analog of the Erd\H{o}s-R\'enyi random graph model. The proposed model is obtained by…
A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two…
Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural sciences. In dynamical networks, phase transitions organize qualitative changes in the collective behavior of coupled dynamical units. Adaptive…
Given a connected network, it can be augmented by applying a growing strategy (e.g. random or scale-free rules) over the previously existing structure. Another approach for augmentation, recently introduced, involves incorporating a direct…
Deep neural networks are strongly over-parameterized, often containing far more weights than required for their task. Although such redundancy can aid optimization, it leads to inefficient deployment and high computational cost, motivating…
Optimal paths play a fundamental role in numerous physical applications ranging from random polymers to brittle fracture, from the flow through porous media to information propagation. Here for the first time we explore the path that is…
Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random…
We investigate the growth of connectivity in a network. In our model, starting with a set of disjoint nodes, links are added sequentially. Each link connects two nodes, and the connection rate governing this random process is proportional…
We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…
We examine the global organization of growing networks in which a new vertex is attached to already existing ones with a probability depending on their age. We find that the network is infinite- or finite-dimensional depending on whether…
We present an analysis of the topologies of a class of networks which are optimal in terms of the requirements of having as short a route as possible between any two nodes while yet keeping the congestion in the network as low as possible.…
Quantum networks will play a key role in distributed quantum information processing. As the network size increases, network-level errors like random breakdown and intentional attack are inevitable; therefore, it is important to understand…
Current network models assume one type of links to define the relations between the network entities. However, many real networks can only be correctly described using two different types of relations. Connectivity links that enable the…