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While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

Physics and Society · Physics 2024-12-20 Zhao Li , Jing Zhang , Jiqiang Zhang , Guozhong Zheng , Weiran Cai , Li Chen

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

Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we…

Statistical Mechanics · Physics 2012-01-20 Heiko Bauke , Cristopher Moore , Jean-Baptiste Rouquier , David Sherrington

Preferential attachment is commonly invoked to explain the emergence of those heavy-tailed degree distributions characteristic of growing network representations of diverse real-world phenomena. Experimentally confirming this hypothesis in…

Social and Information Networks · Computer Science 2021-06-22 Thong Pham , Paul Sheridan , Hidetoshi Shimodaira

In the field of complex networks, hypergraph models have so far received significantly less attention than graphs. However, many real-life networks feature multiary relations (co-authorship, protein reactions) may therefore be modeled way…

Discrete Mathematics · Computer Science 2023-06-07 Frédéric Giroire , Nicolas Nisse , Kostiantyn Ohulchanskyi , Małgorzata Sulkowska , Thibaud Trolliet

We propose a novel method for network inference from partially observed edges using a node-specific degree prior. The degree prior is derived from observed edges in the network to be inferred, and its hyper-parameters are determined by…

Machine Learning · Statistics 2016-02-09 Qingming Tang , Lifu Tu , Weiran Wang , Jinbo Xu

We provide an analytic expression for the quantity described in the title. Namely, we perform a preferential attachment growth process to generate a scale-free network. At each stage we add a new node with $m$ new links. Let $k$ denote the…

Social and Information Networks · Computer Science 2014-08-13 Michael Small

A statistical model assuming a preferential attachment network, which is generated by adding nodes sequentially according to a few simple rules, usually describes real-life networks better than a model assuming, for example, a Bernoulli…

Computation · Statistics 2018-10-01 Clement Lee , Andrew Garbett , Darren J. Wilkinson

We claim that networks are created according to the priority attachment mechanism and we show a simple model which uses the priority attachment to generate both synthetic and close to empirical networks. Priority attachment is a mechanism…

Social and Information Networks · Computer Science 2019-03-07 Mikołaj Morzy , Tomasz Kajdanowicz , Przemysław Kazienko , Grzegorz Miebs , Arkadiusz Rusin

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

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

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 introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…

Combinatorics · Mathematics 2010-03-02 Alois Panholzer , Georg Seitz

Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various…

Machine Learning · Statistics 2018-07-10 Benjamin Bloem-Reddy , Adam Foster , Emile Mathieu , Yee Whye Teh

We consider the estimation of the affine parameter (and power-law exponent) in the preferential attachment model with random initial degrees. We derive the likelihood, and show that the maximum likelihood estimator (MLE) is asymptotically…

Statistics Theory · Mathematics 2017-03-09 Fengnan Gao , Aad van der Vaart

Relevance and importance are the main factors when humans build network connections. We propose an evolutionary network model based on preferential attachment(PA) considering these factors. We analyze and compute several important features…

Physics and Society · Physics 2014-12-25 Weituo Zhang , Chjan Lim

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 use the framework of multivariate regular variation to analyse the extremal behaviour of preferential attachment models. To this end, we follow a directed linear preferential attachment model for a random, heavy-tailed number of steps in…

Probability · Mathematics 2024-08-06 Anja Janßen , Max Ziegenbalg

We propose a simple preferential attachment model of growing network using the complementary probability of Barab\'asi-Albert (BA) model, i.e., $\Pi(k_i) \propto 1-\frac{k_i}{\sum_j k_j}$. In this network, new nodes are preferentially…

Physics and Society · Physics 2016-01-20 A. Lachgar , A. Achahbar

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