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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…

Statistical Mechanics · Physics 2009-11-07 H. Jeong , Z. Neda , A. -L. Barabasi

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…

Physics and Society · Physics 2015-06-22 Timoteo Carletti , Floriana Gargiulo , Renaud Lambiotte

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…

Other Condensed Matter · Physics 2009-11-13 A. Santiago , R. M. Benito

The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…

Social and Information Networks · Computer Science 2020-12-08 Thibaud Trolliet , Frédéric Giroire , Stéphane Pérennes

We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit exponent that is described in terms of…

Probability · Mathematics 2021-10-20 Sayan Banerjee , Mariana Olvera-Cravioto

We present analytical results for the effect of preferential node deletion on the structure of networks that evolve via node addition and preferential attachment. To this end, we consider a preferential-attachment-preferential-deletion…

Physics and Society · Physics 2025-06-24 Barak Budnick , Ofer Biham , Eytan Katzav

We consider a preferential attachment random graph with self-reinforcement. Each time a new vertex comes in, it attaches itself to an old vertex with a probability that is proportional to the sum of the degrees of that old vertex at all…

Probability · Mathematics 2025-07-29 Yogesh Dahiya , Frank den Hollander

We study a new class of preferential attachment trees with \emph{self-reinforcement}. At each time, each vertex is assigned a weight equal to the cumulative sum over past times of an affine function of its degree. A new vertex attaches…

Probability · Mathematics 2026-05-21 Shankar Bhamidi , Remco van der Hofstad , Frank den Hollander , Rounak Ray

A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential…

Discrete Mathematics · Computer Science 2008-11-27 Yong Gao

We propose a simple preferential attachment model of growing network using the complementary probability of Barab\'asi-Albert (BA) model, i.e., $\Pi(k_i) \propto 1-\frac{k_i}{\sum_j k_j}$. In this network, new nodes are preferentially…

Physics and Society · Physics 2016-01-20 A. Lachgar , A. Achahbar

We study the mean length $\ell(k)$ of the shortest paths between a vertex of degree $k$ and other vertices in growing networks, where correlations are essential. In a number of deterministic scale-free networks we observe a power-law…

Statistical Mechanics · Physics 2015-06-24 S. N. Dorogovtsev , J. F. F. Mendes , J. G. Oliveira

We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…

Disordered Systems and Neural Networks · Physics 2007-05-23 N. Berger , C. Borgs , J. T. Chayes , R. M. D'Souza , R. D. Kleinberg

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…

Probability · Mathematics 2018-08-07 Tiandong Wang , Sidney I. Resnick

We consider a preferential attachment model that incorporates an anomaly. Our goal is to understand the evolution of the network before and after the occurrence of the anomaly by studying the influence of the anomaly on the structural…

Physics and Society · Physics 2025-05-07 Qiu Liang , Remco van der Hofstad , Nelly Litvak

We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at…

Statistical Mechanics · Physics 2009-11-07 R. Xulvi-Brunet , I. M. Sokolov

We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of "splitting" nodes of degree $k$ into $k$ nodes of degree 1. Four networks are considered, each…

Physics and Society · Physics 2013-09-25 E. R. Colman , G. J. Rodgers

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…

Statistical Mechanics · Physics 2012-01-20 Heiko Bauke , Cristopher Moore , Jean-Baptiste Rouquier , David Sherrington

Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable…

Applications · Statistics 2025-09-16 Clement Lee

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,…

Methodology · Statistics 2017-12-21 Phyllis Wan , Tiandong Wang , Richard A. Davis , Sidney I. Resnick

A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…

Physics and Society · Physics 2015-09-30 Maria Deijfen , Mathias Lindholm