Related papers: Inhomogeneous Long-Range Percolation for Real-Life…
Very often, when studying topological or dynamical properties of random scale-free networks, it is tacitly assumed that degree-degree correlations are not present. However, simple constraints, such as the absence of multiple edges and…
We study a one parameter family of random graph models that spans a continuum between traditional random graphs of the Erd\H{o}s-R\'enyi type, where there is no underlying structure, and percolation models, where the possible edges are…
A dynamic model of a society is studied where each person is an uncorrelated and non-interacting random walker. A dynamical random graph represents the acquaintance network of the society whose nodes are the individuals and links are the…
We adjust the classical random waypoint mobility model used in the study of telecommunication networks to a more realistic setting by allowing participants of the network to return to popular places and individual homes. We show that the…
We study the effects of mobility on two crucial characteristics in multi-scale dynamic networks: percolation and connection times. Our analysis provides insights into the question, to what extent long-time averages are well-approximated by…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…
Network geometry has strong effects on network dynamics. In particular, the underlying hyperbolic geometry of discrete manifolds has recently been shown to affect their critical percolation properties. Here we investigate the properties of…
Let $\mathbb{G}=\left(\mathbb{V},\mathbb{E}\right)$ be the graph obtained by taking the cartesian product of an infinite and connected graph $G=(V,E)$ and the set of integers $\mathbb{Z}$. We choose a collection $\mathcal{C}$ of finite…
We study large deviations of the size of the largest connected component in a general class of inhomogeneous random graphs with iid weights, parametrized so that the degree distribution is regularly varying. We derive a large-deviation…
Static wireless networks are by now quite well understood mathematically through the random geometric graph model. By contrast, there are relatively few rigorous results on the practically important case of mobile networks, in which the…
Complex networks have played an important role in describing real complex systems since the end of the last century. Recently, research on real-world data sets reports intermittent interaction among social individuals. In this paper, we pay…
Complex networks display various types of percolation transitions. We show that the degree distribution and the degree-degree correlation alone are not sufficient to describe diverse percolation critical phenomena. This suggests that a…
The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…
Long range connections play an essential role in dynamical processes on networks, on the processing of information in biological networks, on the structure of social and economical networks and in the propagation of opinions and epidemics.…
Loops are subgraphs responsible for the multiplicity of paths going from one to another generic node in a given network. In this paper we present an analytic approach for the evaluation of the average number of loops in random scale-free…
Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogeneous Erd\H{o}s-R\'{e}nyi random graphs on the same vertex…
Graph neural networks can accurately predict the chemical properties of many molecular systems, but their suitability for large, macromolecular assemblies such as gels is unknown. Here, graph neural networks were trained and optimised for…
Large-scale coarse-grained molecular dynamics simulations of inhomogeneous gel networks were performed to investigate abnormal butterfly patterns in two-dimensional scattering. The networks were diamond lattice-based with distributions in…
We give the first properties of independent Bernoulli percolation, for oriented graphs on the set of vertices $\Z^d$ that are translation-invariant and may contain loops. We exhibit some examples showing that the critical probability for…
In a model of a connected network on random points in the plane, one expects that the mean length of the shortest route between vertices at distance $r$ apart should grow only as $O(r)$ as $r \to \infty$, but this is not always easy to…