Journal ArticleDOI
Robustness and network evolution--an entropic principle
Lloyd Demetrius,Thomas Manke +1 more
TLDR
An evolutionary model based on entropy as a selective criterion is formulated and it is shown that it predicts the direction of changes in network structure over evolutionary time and accounts for the high degree of robustness and the heterogenous connectivity distribution, which is often observed in biological and technological networks.Abstract:
This article introduces the concept of network entropy as a characteristic measure of network topology. We provide computational and analytical support for the hypothesis that network entropy is a quantitative measure of robustness. We formulate an evolutionary model based on entropy as a selective criterion and show that (a) it predicts the direction of changes in network structure over evolutionary time and (b) it accounts for the high degree of robustness and the heterogenous connectivity distribution, which is often observed in biological and technological networks. Our model is based on Darwinian principles of evolution and preferentially selects networks according to a global fitness criterion, rather than local preferences in classical models of network growth. We predict that the evolutionarily stable states of evolved networks will be characterized by extremal values of network entropy.read more
Citations
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Proceedings ArticleDOI
Random graphs
TL;DR: Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Journal ArticleDOI
Characterization of complex networks: A survey of measurements
TL;DR: In this paper, the authors present a survey of topological features of complex networks, including trajectories in several measurement spaces, correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification.
Journal ArticleDOI
Characterization of complex networks: A survey of measurements
TL;DR: This article presents a survey of measurements capable of expressing the most relevant topological features of complex networks and includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements.
Journal ArticleDOI
Random walks and diffusion on networks
TL;DR: The theory and applications of random walks on networks are surveyed, restricting ourselves to simple cases of single and non-adaptive random walkers, and three main types are distinguished: discrete-time random walks, node-centric continuous-timerandom walks, and edge-centric Continuous-Time random walks.
Journal ArticleDOI
Random walks and diffusion on networks
TL;DR: Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures as discussed by the authors, and they are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can extract information about important entities or dense groups of entities in networks.
References
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Journal ArticleDOI
Emergence of Scaling in Random Networks
TL;DR: A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
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KEGG: Kyoto Encyclopedia of Genes and Genomes
Minoru Kanehisa,Susumu Goto +1 more
TL;DR: The Kyoto Encyclopedia of Genes and Genomes (KEGG) as discussed by the authors is a knowledge base for systematic analysis of gene functions in terms of the networks of genes and molecules.
Journal ArticleDOI
Statistical mechanics of complex networks
TL;DR: In this paper, a simple model based on the power-law degree distribution of real networks was proposed, which was able to reproduce the power law degree distribution in real networks and to capture the evolution of networks, not just their static topology.
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Error and attack tolerance of complex networks
TL;DR: It is found that scale-free networks, which include the World-Wide Web, the Internet, social networks and cells, display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates.