Related papers: Mechanism for linear preferential attachment in gr…
Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes…
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…
Growing synthetic networks that follow power law distributions of a node's degree often involves adding one node at a time. Each node is added to the network with a fixed amount of edges and those edges are frozen for all future time steps.…
Preferential attachment models have been widely studied in complex networks, because they can explain the formation of many networks like social networks, citation networks, power grids, and biological networks, to name a few. Motivated by…
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…
We consider the degree distributions of preferential attachment random graph models with choice similar to those considered in recent work by Malyshkin and Paquette and Krapivsky and Redner. In these models a new vertex chooses $r$ vertices…
We find assimpotics for the first $k$ highest degrees of the degree distribution in an evolving tree model combining the local choice and the preferential attachment. In the considered model, the random graph is constructd in the following…
We propose a model of network growth in which the network is co-evolving together with the dynamics of a quantum mechanical system, namely a quantum walk taking place over the network. The model naturally generalizes the Barab\'{a}si-Albert…
In this paper, we characterise the notion of preferential attachment in networks as action at a distance, and argue that it can only be an emergent phenomenon -- the actual mechanism by which networks grow always being the closing of…
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…
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 obtain closed form expressions for the expected conditional degree distribution and the joint degree distribution of the linear preferential attachment model for network growth in the steady state. We consider the multiple-destination…
This paper provides time-dependent expressions for the expected degree distribution of a given network that is subject to growth, as a function of time. We consider both uniform attachment, where incoming nodes form links to existing nodes…
Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced…
In an affiliation network vertices are linked to attributes and two vertices are declared adjacent whenever they share a common attribute. For example, two customers of an internet shop are called adjacent if they have purchased the same or…
A vertex of a randomly growing graph is called a persistent hub if at all but finitely many moments of time it has the maximal degree in the graph. We establish the existence of a persistent hub in the Barab\'asi--Albert random graph model…
We propose a model that generates a new class of networks exhibiting power-law degree distribution with a spectrum of exponents depending on the number of links ($m$) with which incoming nodes join the existing network. Unlike the…
The scale-free model of Barabasi and Albert gave rise to a burst of activity in the field of complex networks. In this paper, we revisit one of the main assumptions of the model, the preferential attachment rule. We study a model in which…
The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…
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…