Related papers: Inhomogeneous Long-Range Percolation for Real-Life…
Extended-range percolation is a robust percolation process that has relevance for quantum communication problems. In extended-range percolation nodes can be trusted or untrusted. Untrusted facilitator nodes are untrusted nodes that can…
Given a set of snapshots from a temporal network we develop, analyze, and experimentally validate a so-called network interpolation scheme. Our method allows us to build a plausible, albeit random, sequence of graphs that transition between…
In this paper we study weighted distances in scale-free spatial network models: hyperbolic random graphs (HRG), geometric inhomogeneous random graphs (GIRG) and scale-free percolation (SFP). In HRGs, $n=\Theta(\mathrm{e}^{R/2})$ vertices…
We provide a sufficient criterion for the recurrence of spatial random graphs on the real line based on the scarceness of long-edges. In particular, this complements earlier recurrence results obtained by Gracar et al. (Electron. J. Probab.…
Many processes of spreading and diffusion take place on temporal networks, and their outcomes are influenced by correlations in the times of contact. These correlations have a particularly strong influence on processes where the spreading…
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with 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…
Self-similarity and long-range correlations are the remarkable features of the Earth's surface topography. Here we develop an approach based on percolation theory to study the geometrical features of Earth. Our analysis is based on…
In this paper a lattice model for diffusional transport of particles in the interphase cell nucleus is proposed. Dense networks of chromatin fibers are created by three different methods: randomly distributed, non-interconnected obstacles,…
We consider an inhomogeneous Erd\H{o}s-R\'enyi random graph ensemble with exponentially decaying random disconnection probabilities determined by an i.i.d. field of variables with heavy tails and infinite mean associated to the vertices of…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of…
The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynomial decay in the distance between them. Various aspects of…
Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains…
A recent trend in the context of graph theory is to bring theoretical analyses closer to empirical observations, by focusing the studies on random graph models that are used to represent practical instances. There, it was observed that…
Percolation on complex networks is used both as a model for dynamics on networks, such as network robustness or epidemic spreading, and as a benchmark for our models of networks, where our ability to predict percolation measures our ability…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
In graph signal processing, the graph adjacency matrix or the graph Laplacian commonly define the shift operator. The spectral decomposition of the shift operator plays an important role in that the eigenvalues represent frequencies and the…
We describe in detail a new and highly efficient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…