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We present combinatorial approximation algorithms for the weighted correlation clustering problem. In this problem, we have a set of vertices and two weight values for each pair of vertices, denoting their difference and similarity. The…

Data Structures and Algorithms · Computer Science 2025-07-16 Mojtaba Ostovari , Alireza Zarei

We show that not only preferential attachment but also preferential depletion leads to scale-free networks. The resulting degree distribution exponents is typically less than two (5/3) as opposed to the case of the growth models studied…

Physics and Society · Physics 2015-05-27 Christian M. Schneider , Lucilla de Arcangelis , Hans J. Herrmann

In this paper, by both simulations and theoretical predictions we study two and three node (or degree) correlations in random Apollonian network (RAN), which have small-world and scale-free topologies. Using the rate equation approach under…

Statistical Mechanics · Physics 2007-05-23 Zhongzhi Zhang , Shuigeng Zhou

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

This paper presents a fast and simple new 2-approximation algorithm for minimum weighted vertex cover. The unweighted version of this algorithm is equivalent to a well-known greedy maximal independent set algorithm. We prove that this…

Data Structures and Algorithms · Computer Science 2022-09-13 Nate Veldt

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

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

In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…

Physics and Society · Physics 2011-10-11 Zou Zhi-Yun , Liu Peng , Lei Li , Gao Jian-Zhi

Assortativity measures the tendency of a vertex in a network being connected by other vertexes with respect to some vertex-specific features. Classical assortativity coefficients are defined for unweighted and undirected networks with…

Applications · Statistics 2021-01-15 Yelie Yuan , Jun Yan , Panpan Zhang

We propose a growing network model that consists of two tunable mechanisms: growth by merging modules which are represented as complete graphs and a fitness-driven preferential attachment. Our model exhibits the three prominent statistical…

Molecular Networks · Quantitative Biology 2007-07-31 Kazuhiro Takemoto , Chikoo Oosawa

Motivated by widely observed examples in nature, society and software, where groups of already related nodes arrive together and attach to an existing network, we consider network growth via sequential attachment of linked node groups, or…

Statistical Mechanics · Physics 2009-04-30 Vladimir Filkov , Zachary M. Saul , Soumen Roy , Raissa M. D'Souza , Premkumar T. Devanbu

In this work we consider a growing random graph sequence where a new vertex is less likely to join to an existing vertex with high degree and more likely to join to a vertex with low degree. In contrast to the well studied…

Probability · Mathematics 2025-08-27 Antar Bandyopadhyay , Subhabrata Sen

We propose a novel model-selection method for dynamic networks. Our approach involves training a classifier on a large body of synthetic network data. The data is generated by simulating nine state-of-the-art random graph models for dynamic…

Social and Information Networks · Computer Science 2024-05-28 Lourens Touwen , Doina Bucur , Remco van der Hofstad , Alessandro Garavaglia , Nelly Litvak

A general random graph evolution mechanism is defined. The evolution is a combination of the preferential attachment model and the interaction of N vertices (N>=3). A vertex in the graph is characterized by its degree and its weight. The…

Probability · Mathematics 2013-09-18 István Fazekas , Bettina Porvázsnyik

In real life, networks are dynamic in nature; they grow over time and often exhibit power-law degree sequences. To model the evolving structure of the internet, Barab\'{a}si and Albert introduced a simple dynamic model with a power-law…

Probability · Mathematics 2024-11-22 Rounak Ray

We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative…

Condensed Matter · Physics 2009-11-07 Konstantin Klemm , Victor M. Eguiluz

We consider the degree distributions of preferential attachment random graph models with choice similar to those considered in recent work by Malyshkin and Paquette and Krapivsky and Redner. In these models a new vertex chooses $r$ vertices…

Probability · Mathematics 2020-08-12 John Haslegrave , Jonathan Jordan

The configuration model is one of the most successful models for generating uncorrelated random networks. We analyze its behavior when the expected degree sequence follows a power law with exponent smaller than two. In this situation, the…

Disordered Systems and Neural Networks · Physics 2009-11-11 M. A. Serrano , M. Boguna

We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…

Combinatorics · Mathematics 2015-05-20 Liudmila Ostroumova , Alexander Ryabchenko , Egor Samosvat

Many complex natural and physical systems exhibit patterns of interconnection that conform, approximately, to a network structure referred to as scale-free. Preferential attachment is one of many algorithms that have been introduced to…

Physics and Society · Physics 2014-11-18 Linjun Zhang , Michael Small , Kevin Judd