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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…

Physics and Society · Physics 2012-02-08 Vijay K Samalam

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

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…

Probability · Mathematics 2016-08-31 Yury Malyshkin

We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented with information on leafdegree (number of neighbors that are…

Statistical Mechanics · Physics 2026-02-03 Harrison Hartle , P. L. Krapivsky

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…

Statistical Mechanics · Physics 2007-05-23 Claire P. Massen , Jonathan P. K. Doye

We study an asymptotical behavior of the maximal degree in the degree distribution in an evolving tree model combining the local choice and the Mori's preferential attachment. In the considered model, the random graph is constructed in the…

Probability · Mathematics 2017-10-27 Yury Malyshkin

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 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…

Probability · Mathematics 2008-07-31 Steffen Dereich , Peter Morters

We study a random recursive tree model featuring complete redirection called the random friend tree and introduced by Saram\"aki and Kaski. Vertices are attached in a sequential manner one by one by selecting an existing target vertex and…

We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…

Probability · Mathematics 2017-04-20 Sunder Sethuraman , Shankar C. Venkataramani

A dynamic model for a random network evolving in continuous time is defined where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is…

Probability · Mathematics 2015-09-24 Maria Deijfen

We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known…

Probability · Mathematics 2018-05-04 Carina Betken , Hanna Döring , Marcel Ortgiese

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

We introduce a model of evolving preferential attachment trees where vertices are assigned weights, and the evolution of a vertex depends not only on its own weight, but also on the weights of its neighbours. We study the distribution of…

Probability · Mathematics 2021-01-11 Nikolaos Fountoulakis , Tejas Iyer

There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…

Statistical Mechanics · Physics 2011-11-09 Cristopher Moore , Gourab Ghoshal , M. E. J. Newman

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

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.…

Physics and Society · Physics 2026-01-27 Justin Downes

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…

Statistical Mechanics · Physics 2007-05-23 Marcelo D. S. de Meneses , Sharon D. da Cunha , D. J. B. Soares , L. R. da Silva

A variation of the preferential attachment random graph model of Barab\'asi and Albert is defined that incorporates planted communities. The graph is built progressively, with new vertices attaching to the existing ones one-by-one. At every…

Machine Learning · Statistics 2018-01-30 Bruce Hajek , Suryanarayana Sankagiri

Inspired by empirical data on real world complex networks, the last few years have seen an explosion in proposed generative models to understand and explain observed properties of real world networks, including power law degree distribution…

Probability · Mathematics 2015-08-11 Shankar Bhamidi , Jimmy Jin , Andrew Nobel