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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 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 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

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

Real-world networks are rarely static. Recently, there has been increasing interest in both network growth and network densification, in which the number of edges scales superlinearly with the number of nodes. Less studied but equally…

Social and Information Networks · Computer Science 2023-05-10 Haochen Pi , Keith Burghardt , Allon G. Percus , Kristina Lerman

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…

Probability · Mathematics 2015-03-18 Emmanuel Jacob , Peter Mörters

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 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

A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…

Probability · Mathematics 2007-05-23 K. B. Athreya , A. P. Ghosh , S. Sethuraman

Motivated by the complexity of network data, we propose a directed hybrid random network that mixes preferential attachment (PA) rules with uniform attachment (UA) rules. When a new edge is created, with probability $p\in [0,1]$, it follows…

Social and Information Networks · Computer Science 2021-01-19 Tiandong Wang , Panpan Zhang

We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We…

Disordered Systems and Neural Networks · Physics 2009-11-13 Fernando Peruani , Monojit Choudhury , Animesh Mukherjee , Niloy Ganguly

The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse…

Data Analysis, Statistics and Probability · Physics 2009-11-13 Xinping Xu , Feng Liu , Lianshou Liu

Preferential attachment is an appealing mechanism for modeling power-law behavior of the degree distributions in directed social networks. In this paper, we consider methods for fitting a 5-parameter linear preferential model to network…

Methodology · Statistics 2017-08-29 Phyllis Wan , Tiandong Wang , Richard A. Davis , Sidney I. Resnick

We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…

Statistical Mechanics · Physics 2014-04-28 Hans Hooyberghs , Bert Van Schaeybroeck , Joseph O. Indekeu

Generated networks are widely used in network-based research as a convenient simulation environment. Generating universal networks that more accurately reflect real-world patterns is a cornerstone task. This study proposes a vari-linear…

Physics and Society · Physics 2026-04-27 Jinhu Ren , Linyuan Lü

Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced…

Physics and Society · Physics 2013-06-26 James P. Bagrow , Dirk Brockmann

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

In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…

Physics and Society · Physics 2014-11-05 Babak Fotouhi

Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…

Probability · Mathematics 2018-04-18 Angelica Pachon , Laura Sacerdote , Shuyi Yang

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