Related papers: Universality in random quantum networks

Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…

Traditionally, network analysis is based on local properties of vertices, like their degree or clustering, and their statistical behavior across the network in question. This paper develops an approach which is different in two respects. We…

I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…

The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…

Complex networks are ubiquitous in nature and play a role of paramount importance in many contexts. Internet and the cyberworld, which permeate our everyday life, are self-organized hierarchical graphs. Urban traffic flows on intricate road…

This paper provides a necessary and sufficient condition for a random network with nodes Poissonly distributed on a unit square and a pair of nodes directly connected following a generic random connection model to be asymptotically almost…

Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…

We study directed random graphs (random graphs whose edges are directed), and present new results on the so-called strong components of those graphs. We provide analytic and simulation results on two special classes of strong component,…

In quantum information theory there is a construction for quantum channels, appropriately called a quantum graph, that generalizes the confusability graph construction for classical channels in classical information theory. In this paper,…

Network theory has played a dominant role in understanding the structure of complex systems and their dynamics. Recently, quantum complex networks, i.e. collections of quantum systems in a non-regular topology, have been explored leading to…

The problem of predicting links in large networks is an important task in a variety of practical applications, including social sciences, biology and computer security. In this paper, statistical techniques for link prediction based on the…

The characterisation of quantum networks is fundamental to understanding how energy and information propagates through complex systems, with applications in control, communication, error mitigation and energy transfer. In this work, we…

It has been proposed that random wide neural networks near Gaussian process are quantum field theories around Gaussian fixed points. In this paper, we provide a novel map with which a wide class of quantum mechanical systems can be cast…

Online social networks are a dominant medium in everyday life to stay in contact with friends and to share information. In Twitter, users can connect with other users by following them, who in turn can follow back. In recent years,…

Quantum networks are of high interest nowadays and a quantum internet has been long envisioned. Network-entanglement adapts the notion of entanglement to the network scenario and network-entangled states are considered to be a resource to…

Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as…

This study introduces an algorithm that generates undirected graphs with three main characteristics of real-world networks: scale-freeness, short distances between nodes (small-world phenomenon), and large clustering coefficients. The main…

Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…

Many networks describing complex systems are directed: the interactions between elements are not symmetric. Recent work has shown that these networks can display properties such as trophic coherence or non-normality, which in turn affect…

The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that…