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The mechanism of preferential attachment underpins most recent social network formation models. Yet few authors attempt to check or quantify assumptions on this mechanism. We call generalized preferential attachment any kind of preference…
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…
Popularity is attractive -- this is the formula underlying preferential attachment, a popular explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting…
We introduce a network growth model in which the preferential attachment probability includes the fitness vertex and the Euclidean distance between nodes. We grow a planar network around its barycenter. Each new site is fixed in space by…
In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes…
We perform an empirical study of the preferential attachment phenomenon in temporal networks and show that on the Web, networks follow a nonlinear preferential attachment model in which the exponent depends on the type of network…
Large scale real-world network data such as social and information networks are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, and…
The power law has been observed in the degree distributions of many biological neural networks. Sparse deep neural networks, which learn an economical representation from the data, resemble biological neural networks in many ways. In this…
In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…
Modeling complex networks has been the focus of much research for over a decade. Preferential attachment (PA) is considered a common explanation to the self organization of evolving networks, suggesting that new nodes prefer to attach to…
Preferential attachment is the most popular explanation for the emergence of scaling behavior in the World Wide Web, but this explanation has been challenged by the global information hypothesis, the existence of linear preference and the…
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…
This article reviews and evaluates models of network evolution based on the notion of structural diversity. We show that diversity is an underlying theme of three principles of network evolution: the preferential attachment model,…
We highlight intriguing features of complex networks that are grown by \emph{redirection}. In this mechanism, a target node is chosen uniformly at random from the pre-existing network nodes and the new node attaches either to this initial…
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…
Network modeling characterizes the underlying principles of structural properties and is of vital significance for simulating dynamical processes in real world. However, bridging structure and dynamics is always challenging due to the…
We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible…
In this paper, we propose a growing random complex network model, which we call context dependent preferential attachment model (CDPAM), when the preference of a new node to get attached to old nodes is determined by the local and global…
Relevance and importance are the main factors when humans build network connections. We propose an evolutionary network model based on preferential attachment(PA) considering these factors. We analyze and compute several important features…
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…