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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

In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment which has two new properties; first, it encapsulates both the topological and weight aspects of a network,…

Physics and Society · Physics 2007-05-23 Chen Chen

We analyze a dynamic random undirected graph in which newly added vertices are connected to those already present in the graph either using, with probability $p$, an anti-preferential attachment mechanism or, with probability $1-p$, a…

Probability · Mathematics 2020-12-11 Umberto De Ambroggio , Federico Polito , Laura Sacerdote

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

We investigate choice-driven network growth. In this model, nodes are added one by one according to the following procedure: for each addition event a set of target nodes is selected, each according to linear preferential attachment, and a…

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

We study the basic preferential attachment process, which generates a sequence of random trees, each obtained from the previous one by introducing a new vertex and joining it to one existing vertex, chosen with probability proportional to…

Probability · Mathematics 2012-01-31 Graham Brightwell , Malwina J. Luczak

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

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

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…

Disordered Systems and Neural Networks · Physics 2009-11-10 Hrvoje Stefancic , Vinko Zlatic

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

We consider a simple Preferential Attachment graph process, which begins with a finite graph, and in which a new $(t+1)$st vertex is added at each subsequent time step $t$, and connected to each previous vertex $u \leq t$ with probability…

Combinatorics · Mathematics 2020-04-22 Richard Elwes

In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…

Physics and Society · Physics 2012-11-09 Ke Hu , Ju Xiang , Wanchun Yang , Xiaoke Xu , Yi Tang

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 study the asymptotic behavior of the maximum degree in the preferential attachment model with a choice-based edge-step. We add vertex type to the model and prove, among others types of behavior, the effect of condensation on multiple…

Probability · Mathematics 2024-05-31 Yury Malyshkin

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

This paper expands the degree-based consideration of the preferential attachment growth process and applies five different connectivity criteria (node degree, clustering coefficient, betweenness centrality, closeness centrality, and…

Physics and Society · Physics 2020-01-16 Dimitrios Tsiotas

The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two \emph{independent} pure birth processes that are observed at a common exponentially…

Probability · Mathematics 2018-10-08 Tom Britton

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…

Probability · Mathematics 2025-11-25 Chenxu Feng , Yifan Li

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…

Physics and Society · Physics 2016-10-05 Tonći Antunović , Elchanan Mossel , Miklos Z. Racz

We introduce a novel preferential attachment model using the draw variables of a modified P\'olya urn with an expanding number of colors, notably capable of modeling influential opinions (in terms of vertices of high degree) as the graph…

Probability · Mathematics 2024-05-15 Somya Singh , Fady Alajaji , Bahman Gharesifard