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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

Understanding the structure and evolution of online bipartite networks is a significant task since they play a crucial role in various e-commerce services nowadays. Recently, various attempts have been tried to propose different models,…

Physics and Society · Physics 2015-06-11 C. -X. Zhang , Z. -K. Zhang , C. Liu

Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…

Statistical Mechanics · Physics 2009-10-31 D. S. Callaway , M. E. J. Newman , S. H. Strogatz , D. J. Watts

Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…

Social and Information Networks · Computer Science 2013-05-24 Lovro Šubelj , Marko Bajec

Condensation phenomenon is often observed in social networks such as Twitter where one "superstar" vertex gains a positive fraction of the edges, while the remaining empirical degree distribution still exhibits a power law tail. We…

Probability · Mathematics 2015-09-10 Shankar Bhamidi , J. Michael Steele , Tauhid Zaman

We propose a model to create synthetic networks that may also serve as a narrative of a certain kind of infrastructure network evolution. It consists of an initialization phase with the network extending tree-like for minimum cost and a…

Physics and Society · Physics 2016-02-09 Paul Schultz , Jobst Heitzig , Jürgen Kurths

In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhibit leaf proliferation, in which the…

Statistical Mechanics · Physics 2026-04-03 Harrison Hartle , P. L. Krapivsky , S. Redner , Yuanzhao Zhang

Online social networks are a dominant medium in everyday life to stay in contact with friends and to share information. In Twitter, users can connect with other users by following them, who in turn can follow back. In recent years,…

Social and Information Networks · Computer Science 2022-05-06 Christoph Schweimer , Christine Gfrerer , Florian Lugstein , David Pape , Jan A. Velimsky , Robert Elsässer , Bernhard C. Geiger

We present exact results for the degree distribution in a directed network model that grows by node duplication (ND). Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific…

Physics and Society · Physics 2019-08-21 Chanania Steinbock , Ofer Biham , Eytan Katzav

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

For most networks, the connection between two nodes is the result of their mutual affinity and attachment. In this paper, we propose a mutual selection model to characterize the weighted networks. By introducing a general mechanism of…

Statistical Mechanics · Physics 2009-11-11 Wen-Xu Wang , Bu Hu , Tao Zhou , Bing-Hong Wang , Yan-Bo Xie

In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…

Combinatorics · Mathematics 2014-01-07 Linda Farczadi , Nicholas Wormald

We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s, for any…

Statistical Mechanics · Physics 2007-10-18 M. E. J. Newman

Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law…

Physics and Society · Physics 2021-05-24 Xiaojun Zhang , Zheng He , Liwei Zhang , Lez Rayman-Bacchus , Yue Xiao , Shuhui Shen

Identifying power-law scaling in real networks - indicative of preferential attachment - has proved controversial. Critics argue that measuring the temporal evolution of a network directly is better than measuring the degree distribution…

Preferential attachment is a popular generative mechanism to explain the widespread observation of power law distributed networks. We introduce an alternative explanation for the phenomenon by allowing the link growth rates to vary across…

Physics and Society · Physics 2007-06-18 Birgitte Freiesleben de Blasio , Odd O Aalen

Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the…

Physics and Society · Physics 2009-11-11 Michael Schnegg

We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…

Statistics Theory · Mathematics 2013-06-07 Sofia C. Olhede , Patrick J. Wolfe

The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and…

Physics and Society · Physics 2025-07-11 Jonathan Franceschi , Lorenzo Pareschi , Mattia Zanella

Our work introduces an approach for estimating the contribution of attachment mechanisms to the formation of growing networks. We present a generic model in which growth is driven by the continuous attachment of new nodes according to…

Probability · Mathematics 2019-02-20 Jan Medina , Jorge Finke , Camilo Rocha