Related papers: Phase transition in preferential attachment-detach…
We study a general preferential attachment and Polya's urn model. At each step a new vertex is introduced, which can be connected to at most one existing vertex. If it is disconnected, it becomes a pioneer vertex. Given that it is not…
We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We…
We study the asymptotic behavior of the maximal in-degree in the spatial preferential attachment model with a choice-based edge step. We prove different types of behavior of maximal in-degree based on the model's parameters.
We investigate spatial random graphs defined on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit exponent that is described in terms of…
Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are…
Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable…
In this paper we focus on the problem of the degree sequence for the following random graph process. At any time-step $t$, one of the following three substeps is executed: with probability $\alpha_1$, a new vertex $x_t$ and $m$ edges…
We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model taking place on spatially embedded networks. These structures are built from an underlying regular…
We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…
We derive the full phase diagram for a large family of two-parameter exponential random graph models, each containing a first order transition curve ending in a critical point.
We propose a simple random process inducing various types of random graphs and the scale free random graphs among others. The model is of a threshold nature and differs from the preferential attachment approach discussed in the literature…
The article deals with two classes of growing random graphs following the preferential attachment rule with a linear weight function, L-graphs, and hybrid Pennock graphs. We determine the exact final vertex degree distribution and the exact…
We introduce a network growth model in which the preferential attachment probability includes the fitness vertex and the Euclidean distance between nodes. We grow a planar network around its barycenter. Each new site is fixed in space by…
We study the first-passage properties of a jump process with constant drift where jump amplitudes and inter-arrival times follow arbitrary light-tailed distributions with smooth densities. Using a mapping to an effective discrete-time…
We propose a model to create synthetic networks that may also serve as a narrative of a certain kind of infrastructure network evolution. It consists of an initialization phase with the network extending tree-like for minimum cost and a…
We consider the behaviour of open quantum systems in dependence on the coupling to one decay channel by introducing the coupling parameter $\alpha$ being proportional to the average degree of overlapping. Under critical conditions, a…
We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…
In the Constrained-degree percolation model on a graph $(\mathbb{V},\mathbb{E})$ there are a sequence, $(U_e)_{e\in\mathbb{E}}$, of i.i.d. random variables with distribution $U[0,1]$ and a positive integer $k$. Each bond $e$ tries to open…