Related papers: Anomalous Transport in Complex Networks
Random network models generated using sparse exchangeable graphs have provided a mechanism to study a wide variety of complex real-life networks. In particular, these models help with investigating power-law properties of degree…
We propose a model to create synthetic networks that may also serve as a narrative of a certain kind of infrastructure network evolution. It consists of an initialization phase with the network extending tree-like for minimum cost and a…
A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential…
A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree $k$ follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$. However,…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
The behaviour of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
Many social, technological, biological, and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most…
Disordered systems have grown in importance in the past decades, with similar phenomena manifesting themselves in many different physical systems. Because of the difficulty of the topic, theoretical progress has mostly emerged from…
We study the large-deviation properties of minimum spanning trees for two ensembles of random graphs with $N$ nodes. First, we consider complete graphs. Second, we study Erd\H{o}s-R\'{e}nyi (ER) random graphs with edge probability $p=c/N$…
Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…
Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that…
Despite great effort spent measuring topological features of large networks like the Internet, it was recently argued that sampling based on taking paths through the network (e.g., traceroutes) introduces a fundamental bias in the observed…
We study message transport on a $1-d$ ring of nodes and randomly distributed hubs. Messages are deposited on the network at a constant rate. When the rate at which messages are deposited on the lattice is very high, messages start…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
Every route of a transport network approaching equilibrium can be represented by a vector of Euclidean space which length quantifies its segregation from the rest of the graph. We have empirically observed that the distribution of lengths…
Scale-free networks are characterized by a degree distribution with power-law behavior and have been shown to arise in many areas, ranging from the World Wide Web to transportation or social networks. Degree distributions of observed…
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 determine analytically the distribution of conductances of quasi one-dimensional disordered electron systems, neglecting electron-electron interaction, for all strengths of disorder. We find that in the crossover region between the…
We propose an analytically tractable neural connectivity model with power-law distributed synaptic strengths. When threshold neurons with biologically plausible number of incoming connections are considered, our model features a continuous…