Related papers: Preferential attachment with choice based edge-ste…
We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses…
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 investigate the degree sequences of geometric preferential attachment graphs in general compact metric spaces. We show that, under certain conditions on the attractiveness function, the behaviour of the degree sequence is similar to that…
Preferential attachment is an appealing edge generating mechanism for modeling social networks. It provides both an intuitive description of network growth and an explanation for the observed power laws in degree distributions. However,…
A network growth mechanism based on a two-step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required. In the first filtering step a subset of fixed size $m$ of existing nodes…
The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…
The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two \emph{independent} pure birth processes that are observed at a common exponentially…
We consider the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms $m$ connections. The neighbors of the new vertex are chosen at random with probability proportional to…
We study a random graph model with preferential edge attachment and detachment through the embedding into a generalized Yule model. We show that the in-degree distribution of a vertex chosen uniformly at random follows a power law in the…
We propose a preferential attachment model for network growth where new entering nodes have a partial information about the state of the network. Our main result is that the presence of bounded information modifies the degree distribution…
In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the…
We extend the work of Antunovi\'{c}, Mossel and R\'{a}cz on competing types in preferential attachment models to include cases where the types have different fitnesses, which may be either multiplicative or additive. We will show that,…
Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…
We obtain the degree distribution for a class of growing network models on flat and curved spaces. These models evolve by preferential attachment weighted by a function of the distance between nodes. The degree distribution of these models…
In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
A key ingredient of current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called…
We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We…
We examine the effects of preferential attachment on a model of competing clusters. In the original model, cluster masses grow at the expense of their neighbours; on a lattice, this is known to result in the asymptotic survival and…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…