相关论文: Near critical preferential attachment networks hav…

We study properties of some standard network models when the population is split into two types and the connection pattern between the types is varied. The studied models are generalizations of the Erd\H{o}s-R\'{e}nyi graph, 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…

We introduce a new oriented evolving graph model inspired by biological networks. A node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes. This leads to a statistical…

We investigate a growing network model that combines preferential and uniform attachment with two distinct mechanisms of edge deletion. In addition to the usual uniform probability edge deletion, we introduce a novel node-based rule in…

We consider a large class of spatially-embedded random graphs that includes among others long-range percolation, continuum scale-free percolation and the age-dependent random connection model. We assume that the model is supercritical:…

Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…

Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…

We show that not only preferential attachment but also preferential depletion leads to scale-free networks. The resulting degree distribution exponents is typically less than two (5/3) as opposed to the case of the growth models studied…

We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scaling corresponds to the p=c/n scaling for G(n,p)…

Analytical results are presented for the structure of networks that evolve via a preferential-attachment-random-deletion (PARD) model in the regime of overall network growth and in the regime of overall contraction. The phase transition…

Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…

Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we…

We identify the size of the largest connected component in a subcritical inhomogeneous random graph with a kernel of preferential attachment type. The component is polynomial in the graph size with an explicitly given exponent, which is…

We determine the asymptotic size of the largest component in the $2$-type binomial random graph $G(\mathbf{n},P)$ near criticality using a refined branching process approach. In $G(\mathbf{n},P)$ every vertex has one of two types, the…

Many networks exhibit scale free behavior where their degree distribution obeys a power law for large vertex degrees. Models constructed to explain this phenomena have relied on preferential attachment where the networks grow by the…

The voter model is a classical interacting particle system, modelling how global consensus is formed by local imitation. We analyse the time to consensus for a particular family of voter models when the underlying structure is a scale-free…

If we add links to a network at random, a critical threshold can be crossed where a giant connected component forms. Conversely, if links or nodes are removed at random, the giant component shrinks and eventually breaks. In this paper, we…

The percolation phase transition in complex network systems attracts much attention and has numerous applications in various research fields. Finite size effects smooth the transition and make it difficult to predict the critical point of…

We study random digraphs on sequences of expanders with bounded average degree {which converge locally in probability}. We prove that the threshold for the existence of a giant strongly connected component, as well as the asymptotic…

A wide array of random graph models have been postulated to understand properties of observed networks. Typically these models have a parameter $t$ and a critical time $t_c$ when a giant component emerges. It is conjectured that for a large…