Related papers: A geometric preferential attachment model with fit…
We provide an analytic expression for the quantity described in the title. Namely, we perform a preferential attachment growth process to generate a scale-free network. At each stage we add a new node with $m$ new links. Let $k$ denote the…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
Numerous works have been proposed to generate random graphs preserving the same properties as real-life large scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs…
In the classical Erd\"os-R\'enyi random graph G(n,p) there are n vertices and each of the possible edges is independently present with probability p. The random graph G(n,p) is homogeneous in the sense that all vertices have the same…
We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by…
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…
Edge expansion is a parameter indicating how well-connected a graph is. It is useful for designing robust networks, analysing random walks or information flow through a network and is an important notion in theoretical computer science.…
In this paper we define a family of preferential attachment models for random graphs with fitness in the following way: independently for each node, at each time step a random fitness is drawn according to the position of a moving average…
We consider subgraph counts in general preferential attachment models with power-law degree exponent $\tau>2$. For all subgraphs $H$, we find the scaling of the expected number of subgraphs as a power of the number of vertices. We prove our…
We study a generalization of the affine preferential attachment model where triangles are randomly added to the graph. We show that the model exhibits an asymptotically power-law degree distribution with adjustable parameter $\gamma\in…
We introduce a new class of countably infinite random geometric graphs, whose vertices are points in a metric space, and vertices are adjacent independently with probability p if the metric distance between the vertices is below a given…
We study two models of growing recursive trees. For both models, initially the tree only contains one vertex $u_1$ and at each time $n\geq 2$ a new vertex $u_n$ is added to the tree and its parent is chosen randomly according to some rule.…
We consider a preferential attachment model that incorporates an anomaly. Our goal is to understand the evolution of the network before and after the occurrence of the anomaly by studying the influence of the anomaly on the structural…
We consider linear preferential attachment random trees with additive fitness, where fitness is defined as the random initial vertex attractiveness. We show that when the fitness distribution has positive bounded support, the weak local…
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…
In this paper, we prove the first-order convergence law for the uniform attachment random graph with almost all vertices having the same degree. In the considered model, vertices and edges are introduced recursively: at time $m+1$ we start…
We extend the classical preferential attachment random graph model to random simplicial complexes. At each stage of the model, we choose one of the existing $k$-simplices with probability proportional to its $k$-degree. The chosen…
We introduce a model of a preferential attachment based random graph which extends the family of models in which condensation phenomena can occur. Each vertex has an associated uniform random variable which we call its location. Our model…
We study a generalisation of the random recursive tree (RRT) model and its multigraph counterpart, the uniform directed acyclic graph (DAG). Here, vertices are equipped with a random vertex-weight representing initial inhomogeneities in the…
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…