Related papers: Graph distances in scale-free percolation: the log…
In this paper we are interested in an intrinsic property of graphs which is derived from their embeddings into the Euclidean 3-space $\mathbb{R}^3$. An embedding of a graph into $\mathbb{R}^3$ is said to be linear, if it sends every edge to…
The stochastic Kronecker Graph model can generate large random graph that closely resembles many real world networks. For example, the output graph has a heavy-tailed degree distribution, has a (low) diameter that effectively remains…
The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to…
A distance graph is an undirected graph on the integers where two integers are adjacent if their difference is in a prescribed distance set. The independence ratio of a distance graph $G$ is the maximum density of an independent set in $G$.…
We study the evolution of random graphs where edges are added one by one between pairs of weighted vertices so that resulting graphs are scale-free with the degree exponent $\gamma$. We use the branching process approach to obtain scaling…
We study the emergence of a giant component in a spatial network where the distribution of the metric distances between the nodes is scale-invariant, and the interaction between the nodes has a long-range power-law behavior. The nodes are…
We study a random graph model which combines properties of the edge percolation model on Z^d and a classical random graph G(n,c/n). We show that this model, being a homogeneous random graph, has a natural relation to the so-called "rank 1…
We study transport properties such as electrical and frictionless flow conductance on scale-free and Erdos-Renyi networks. We consider the conductance G between two arbitrarily chosen nodes where each link has the same unit resistance. Our…
We extend the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the…
In this paper we study first-passage percolation in the configuration model with empirical degree distribution that follows a power-law with exponent $\tau \in (2,3)$. We assign independent and identically distributed (i.i.d.)\ weights to…
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…
Statistical graph models aim at modeling graphs as random realization among a set of possible graphs. One issue is to evaluate whether or not a graph is likely to have been generated by one particular model. In this paper we introduce the…
With a view on graph clustering, we present a definition of vertex-to-vertex distance which is based on shared connectivity. We argue that vertices sharing more connections are closer to each other than vertices sharing fewer connections.…
To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison…
Spatial models for areal data are often constructed such that all pairs of adjacent regions are assumed to have near-identical spatial autocorrelation. In practice, data can exhibit dependence structures more complicated than can be…
We study an inhomogeneous random connection model in the connectivity regime. The vertex set of the graph is a homogeneous Poisson point process $\mathcal{P}_s$ of intensity $s>0$ on the unit cube…
There is a pressing need for a description of complex systems that includes considerations of the underlying network of interactions, for a diverse range of biological, technological and other networks. In this work relationships between…
Real-world networks, e.g. the social relations or world-wide-web graphs, exhibit both small-world and scale-free behaviour. We interpret lattice triangulations as planar graphs by identifying triangulation vertices with graph nodes and…
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…
A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being…