Related papers: On dynamic random graphs with degree homogenizatio…
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 consider a model of random tree growth, where at each time unit a new vertex is added and attached to an already existing vertex chosen at random. The probability with which a vertex with degree $k$ is chosen is proportional to $w(k)$,…
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…
This paper analyzes key properties of networks generated by geometric preferential attachment. We establish that the expected number of triangles is proportional to that of the standard preferential attachment model, with a proportionality…
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great…
The goal of is to study how increased variability in the degree distribution impacts the global connectivity properties of a large network. We approach this question by modeling the network as a uniform random graph with a given degree…
Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that…
We discuss several limiting degree distributions for a class of random threshold graphs in the many node regime. This analysis is carried out under a weak assumption on the distribution of the underlying fitness variable. This assumption,…
Preferential attachment networks are a type of random network where new nodes are connected to existing ones at random, and are more likely to connect to those that already have many connections. We investigate further a family of models…
We study preferential attachment models where vertices enter the network with i.i.d. random numbers of edges that we call the out-degree. We identify the local limit of such models, substantially extending the work of Berger et al.(2014).…
A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the…
We study the degree distribution of a randomly chosen vertex in a duplication--divergence graph, under a variety of different generalizations of the basic model of Bhan, Galas and Dewey (2002) and V\'azquez, Flammini, Maritan and Vespignani…
In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…
Random planar graphs have been the subject of much recent work. Many basic properties of the standard uniform random planar graph P_{n}, by which we mean a graph chosen uniformly at random from the set of all planar graphs with vertex set…
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…
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…
Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. In a directed preferential attachment model, despite the well-known marginal power-law degree…
We introduce and analyse a Dynamic Random Graph with Vertex Removal (DRGVR) defined as follows. At every step, with probability $p > 1/2$ a new vertex is introduced, and with probability $1-p$ a vertex, chosen uniformly at random among the…
A probabilistic generative network model with $n$ nodes and $m$ overlapping layers is obtained as a superposition of $m$ mutually independent Bernoulli random graphs of varying size and strength. When $n$ and $m$ are large and of the same…
Preferential attachment probabilities scheme appear in the context of scale free random graphs [1],[2]. In this work we present preferential attachment probabilities scheme as a sequence of dependent Bernoulli random variables and we give…