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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…

Physics and Society · Physics 2025-01-14 P. L. Krapivsky , S. Redner

A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the…

Physics and Society · Physics 2023-09-04 Dahae Roh , Kwang-Il Goh

We study randomly growing trees governed by the affine preferential attachment rule. Starting with a seed tree $S$, vertices are attached one by one, each linked by an edge to a random vertex of the current tree, chosen with a probability…

Probability · Mathematics 2018-11-01 David Corlin Marchand , Ioan Manolescu

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment…

Probability · Mathematics 2017-11-10 Alessandro Garavaglia , Remco van der Hofstad , Gerhard Woeginger

We investigate a variety of statistical properties associated with the number of distinct degrees that exist in a typical network for various classes of networks. For a single realization of a network with N nodes that is drawn from an…

Statistical Mechanics · Physics 2014-01-03 P. L. Krapivsky , S. Redner

We propose a new preferential attachment-based network growth model in order to explain two properties of growing networks: (1) the power-law growth of node degrees and (2) the decay of node relevance. In preferential attachment models, the…

Physics and Society · Physics 2018-04-10 Jun Sun , Steffen Staab , Fariba Karimi

We investigate the growth of a class of networks in which a new node first picks a mediator at random and connects with $m$ randomly chosen neighbors of the mediator at each time step. We show that degree distribution in such a…

Physics and Society · Physics 2016-11-29 Md. Kamrul Hassan , Liana Islam , Syed Arefinul Haque

Growing network models with preferential attachment dependent on both age and degree are proposed to simulate certain features of citation network noted in \cite{red2}. In this directed network, a new node gets attached to an older node…

Physics and Society · Physics 2015-06-26 Kamalika Basu Hajra , Parongama Sen

In this paper, we analyze assortativity of preferential attachment models. We deal with a wide class of preferential attachment models (PA-class). It was previously shown that the degree distribution in all models of the PA-class follows a…

Probability · Mathematics 2017-07-07 Alexander Krot , Liudmila Ostroumova Prokhorenkova

We analyze growing networks that are built by enhanced redirection. Nodes are sequentially added and each incoming node attaches to a randomly chosen 'target' node with probability 1-r, or to the parent of the target node with probability…

Statistical Mechanics · Physics 2014-07-25 Alan Gabel , P. L. Krapivsky , S. Redner

Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…

Statistical Mechanics · Physics 2007-05-23 N. Berger , C. Borgs , J. T. Chayes , R. M. D'Souza , R. D. Kleinberg

Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured…

Social and Information Networks · Computer Science 2025-11-25 Yuhan Li , Minyu Feng , Jürgen Kurths

We study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree. Each node is associated with, or "attracted" to its neighbor of maximal degree, as long as the degree is increasing.…

Disordered Systems and Neural Networks · Physics 2008-12-30 Shai Carmi , P. L. Krapivsky , Daniel ben-Avraham

We compute the stationary in-degree probability, $P_{in}(k)$, for a growing network model with directed edges and arbitrary out-degree probability. In particular, under preferential linking, we find that if the nodes have a light tail…

Physics and Society · Physics 2008-10-21 Daniel Fraiman

In this paper we present a framework for the extension of the preferential attachment (PA) model to heterogeneous complex networks. We define a class of heterogeneous PA models, where node properties are described by fixed states in an…

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

Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…

Physics and Society · Physics 2011-08-09 Ke Deng , Ke Hu , Yi Tang

Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. Practical analyses on the tail exponent of the power-law degree distribution use the Hill estimator as one…

Probability · Mathematics 2017-11-17 Tiandong Wang , Sidney Resnick

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…

Machine Learning · Computer Science 2018-05-08 Lu Hou , James T. Kwok

We study the growth of a directed transportation network, such as a food web, in which links carry resources. We propose a growth process in which new nodes (or species) preferentially attach to existing nodes with high indegree (in…

Statistical Mechanics · Physics 2008-03-17 Volkan Sevim , Per Arne Rikvold

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…

Social and Information Networks · Computer Science 2016-05-03 Sushmita Ruj , Arindam Pal