The Structure and Function of Complex Networks

  title={The Structure and Function of Complex Networks},
  author={Mark E. J. Newman},
  journal={SIAM Rev.},
  • M. Newman
  • Published 25 March 2003
  • Computer Science
  • SIAM Rev.
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical… 
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The structure and function of networks
Structural transitions in scale-free networks.
A scaling theory is presented to describe the behavior of the generalized models and the mean-field rate equation for clustering and it is solved for a specific case with the result C(k) approximately 1/k for the clustering of a node of degree k.
Topology of evolving networks: local events and universality
A continuum theory is proposed that predicts the connectivity distribution of the network describing the professional links between movie actors as well as the scaling function and the exponents, in good agreement with numerical results.
Highly clustered scale-free networks.
  • K. Klemm, V. Eguíluz
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2002
The model shows stylized features of real-world networks: power-law distribution of degree, linear preferential attachment of new links, and a negative correlation between the age of a node and its link attachment rate.
Properties of a growing random directed network
Numerically it is confirmed numerically that the distributions of in- and out-degree are consistent with a power law, in agreement with previous analytical results and with empirical measurements from real graphs.
Evolution of networks
The recent rapid progress in the statistical physics of evolving networks is reviewed, and how growing networks self-organize into scale-free structures is discussed, and the role of the mechanism of preferential linking is investigated.
Epidemic spreading in correlated complex networks.
A dynamical model of epidemic spreading on complex networks in which there are explicit correlations among the node's connectivities finds an epidemic threshold inversely proportional to the largest eigenvalue of the connectivity matrix that gives the average number of links.
Emergence of scaling in random networks
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.
Networks in life: Scaling properties and eigenvalue spectra
Topology and correlations in structured scale-free networks.
It is found that the connectivity probability distribution strongly depends on the fine details of the model and exactly the case of low average connectivity is solved, providing also exact expressions for the clustering and degree correlation functions.