ID: 1203.1349

The Evolution of Complex Networks: A New Framework

March 6, 2012

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Statistical mechanics of complex networks

June 6, 2001

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Reka Albert, Albert-Laszlo Barabasi
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cond-mat.dis-nn
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nlin.AO
physics.data-an

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the f...

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The nature and nurture of network evolution

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Bin Zhou, Petter Holme, Zaiwu Gong, Choujun Zhan, Yao Huang, ... , Meng Xiangyi
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Although the origin of the fat-tail characteristic of the degree distribution in complex networks has been extensively researched, the underlying cause of the degree distribution characteristic across the complete range of degrees remains obscure. Here, we propose an evolution model that incorporates only two factors: the node's weight, reflecting its innate attractiveness (nature), and the node's degree, reflecting the external influences (nurture). The proposed model provid...

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A Stochastic Evolutionary Model Exhibiting Power-Law Behaviour with an Exponential Cutoff

September 19, 2002

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Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer'' phenomenon. Despite the generality of the proposed stochastic models, there are still some unexplained phenomena, which may arise due to the limited size of networks such as protein and e-mail networks. Such networks may in fact exhi...

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Ranking in evolving complex networks

April 26, 2017

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Hao Liao, Manuel Sebastian Mariani, Matus Medo, ... , Zhou Ming-Yang
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Complex networks have emerged as a simple yet powerful framework to represent and analyze a wide range of complex systems. The problem of ranking the nodes and the edges in complex networks is critical for a broad range of real-world problems because it affects how we access online information and products, how success and talent are evaluated in human activities, and how scarce resources are allocated by companies and policymakers, among others. This calls for a deep underst...

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A Model for Collaboration Networks Giving Rise to a Power Law Distribution with an Exponential Cutoff

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Trevor Fenner, Mark Levene, George Loizou
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Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer'' phenomenon. Despite the generality of the proposed stochastic models, there are still some unexplained phenomena, which may arise due to the limited size of networks such as protein, e-mail, actor and collaboration networks. Such net...

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"Winner takes it all": strongest node rule for evolution of scale free networks

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H. Stefancic, V. Zlatic
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We study a novel model for evolution of complex networks. We introduce information filtering for reduction of the number of available nodes to a randomly chosen sample, as stochastic component of evolution. New nodes are attached to the nodes that have maximal degree in the sample, which is a deterministic component of network evolution process. This fact is a novel for evolution of scale free networks and depicts a possible new route for modeling network growth. We present b...

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Dynamics-Driven Evolution to Structural Heterogeneity in Complex Networks

April 20, 2008

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Zhen ITP-Cas Shao, Haijun ITP-Cas Zhou
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The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local mutations have higher chances of getting integrated into its structure, the system can evolve into a highly heterogeneous small-world with a global hub (whose connectivity is proportional to the network size), strong local connection corre...

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Composite Centrality: A Natural Scale for Complex Evolving Networks

November 16, 2012

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Andreas Joseph, Guanrong Chen
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We derive a composite centrality measure for general weighted and directed complex networks, based on measure standardisation and invariant statistical inheritance schemes. Different schemes generate different intermediate abstract measures providing additional information, while the composite centrality measure tends to the standard normal distribution. This offers a unified scale to measure node and edge centralities for complex evolving networks under a uniform framework. ...

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The World-Trade Web: Topological Properties, Dynamics, and Evolution

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This paper studies the statistical properties of the web of import-export relationships among world countries using a weighted-network approach. We analyze how the distributions of the most important network statistics measuring connectivity, assortativity, clustering and centrality have co-evolved over time. We show that all node-statistic distributions and their correlation structure have remained surprisingly stable in the last 20 years -- and are likely to do so in the fu...

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A dynamic model of time-dependent complex networks

January 28, 2009

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Scott A. Hill, Dan Braha
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The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness against failures, vulnerability to deliberate attacks, and diffusion properties. However, recent empirical research of large dynamic networks (characterized by connections that are irregular and evolve rapidly) has demonstrated that there i...

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