Related papers: Erdos-Renyi random graphs + forest fires = self-or…
The evolution of the Erd\H{o}s-R\'enyi (ER) network by adding edges can be viewed as a cluster aggregation process. Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection…
Generating function equation has been derived for the probability distribution of the number of nodes with $k \ge 0$ outgoing lines in randomly evolving special trees. The stochastic properties of end-nodes (k=0) have been analyzed, and it…
This paper is a direct continuation of an earlier work, where we studied Erd\"os-R\'enyi random graphs perturbed by an interaction Hamiltonian favouring the formation of short cycles. Here, we generalize these results. We keep the same…
Graph burning is a discrete process that models the spread of influence through a network using a fire as a proxy for the type of influence being spread. This process was recently extended to hypergraphs. We introduce a variant of…
The location and nature of the percolation transition in random networks is a subject of intense interest. Recently, a series of graph evolution processes have been introduced that lead to discontinuous percolation transitions where the…
Motivated by an application in community detection, we consider an \ER random graph conditioned on the rare event that all connected components are fully connected. Such graphs can be considered as partitions of vertices into cliques.…
We address the question of understanding the effect of the underlying network topology on the spread of a virus and the dissemination of information when users are mobile performing independent random walks on a graph. To this end we…
The self-organized critical state is characterized by a power law distribution of cluster sizes and other properties. However experiments with sand and rice piles reveal distributions of avalanche sizes which are not power law distributed.…
We consider two stochastic processes, the Gribov process and the general epidemic process, that describe the spreading of an infectious disease. In contrast to the usually assumed case of short-range infections that lead, at the critical…
We consider the criticality for firing structures of a simplified integrate-and-fire neural model on the regular network, small-world network, and random networks. We simplify an integrate-and-fire model suggested by Levina, Herrmann and…
We consider a sequence of Poisson cluster point processes on $\mathbb{R}^d$: at step $n\in\mathbb{N}_0$ of the construction, the cluster centers have intensity $c/(n+1)$ for some $c>0$, and each cluster consists of the particles of a…
We generalize the asymptotic behavior of the graph distance between two uniformly chosen nodes in the configuration model to a wide class of random graphs. Among others, this class contains the Poissonian random graph, the expected degree…
Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given `far away' observations. Several theoretical results (and simple algorithms) are available when…
Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…
We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick model. These models are built on a…
We study intersection properties of two or more independent tree-like random graphs. Our setting encompasses critical, possibly long range, Bernoulli percolation clusters, incipient infinite clusters, as well as critical branching random…
We investigate an extremal dynamics model of evolution with a variable number of units. Due to addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly…
We consider a system of phase oscillators with random intrinsic frequencies coupled through sparse random networks, and investigate how the connectivity disorder affects the nature of collective synchronization transitions. Various…
In quantum gravity, we study the evolution of a two-dimensional planar open frozen spin network, in which the color (i.e. the twice spin of an edge) labeling edge changes but the underlying graph remains fixed. The mainly considered…
We show that large, slowly driven systems can evolve to a self-organized critical state where long range temporal correlations between bursts or avalanches produce low frequency $1/f^{\alpha}$ noise. The avalanches can occur instantaneously…