Related papers: Levy geometric graphs
We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [Tadi\'c, Physica A {\bf 293},…
The concepts of scale invariance, self-similarity and scaling have been fruitfully applied to the study of price fluctuations in financial markets. After a brief review of the properties of stable Levy distributions and their applications…
Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…
Once recognizing that point particles moving inside the extended version of the rippled billiard perform L\'evy flights characterized by a L\'evy-type distribution $P(\ell)\sim \ell^{-(1+\alpha)}$ with $\alpha=1$, we derive a generalized…
The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations…
We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…
The paper presents a multidimensional model for nonlinear Markovian random walks that generalizes one we developed previously (Phys. Rev. E v.79, 011110, 2009) in order to describe the Levy type stochastic processes in terms of continuous…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
We study the evolution of graphs densifying by adding edges: Two vertices are chosen randomly, and an edge is (i) established if each vertex belongs to a tree; (ii) established with probability $p$ if only one vertex belongs to a tree;…
The L\'evy walk is a non-Brownian random walk model that has been found to describe anomalous dynamic phenomena in diverse fields ranging from biology over quantum physics to ecology. Recurrently occurring problems are to examine whether…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
Representation learning of static and more recently dynamically evolving graphs has gained noticeable attention. Existing approaches for modelling graph dynamics focus extensively on the evolution of individual nodes independently of the…
The L\'evy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha>1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a…
Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or…
A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open…
What distribution of graphical degree sequence is invariant under ``scaling''? Are these graphs always power-law graphs? We show the answer is a surprising ``yes'' for sparse graphs if we ignore isolated vertices, or more generally, the…
Traditional classification tasks learn to assign samples to given classes based solely on sample features. This paradigm is evolving to include other sources of information, such as known relations between samples. Here we show that, even…
We consider random geometric graphs on the plane characterized by a non-uniform density of vertices. In particular, we introduce a graph model where $n$ vertices are independently distributed in the unit disc with positions, in polar…
We consider a random object that is associated with both random walks and random media, specifically, the superposition of a configuration of subcritical Bernoulli percolation on an infinite connected graph and the trace of the simple…
In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a Poisson process approximation that, for graphs which have independent edges, with a possibly…