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… 

Networks and Dynamics: The Structure of the World We Live In

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Evolution of Social Networks

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An Introduction to Complex Networks

The percolation models on the scale-free networks are considered to show how the critical probability and critical behavior change with network topology.

Scale-Free Networks with Different Types of Nodes

This paper proposes a simple model with different types of nodes and deterministic selective linking rule, and makes the model become the weighted network by giving the links the weight and analyze the probability distribution of the node strength.

Metrics and Models for Social Networks

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The “New” Science of Networks

In recent years, the analysis and modeling of networks, and also networked dynamical systems, have been the subject of considerable interdisciplinary interest, yielding several hundred papers in

The Structure of Social Networks

By coupling network theory, game theory and evolutionary algorithms, the role that social networks play in the emergence of social norms is examined and it is shown that analysing the patterns of interconnections between agents can be used to detect dominance relationships.

Networks formed from interdependent networks

Aspects concerning the structure and behaviours of individual networks have been studied intensely in the past decade, but the exploration of interdependent systems in the context of complex networks

Structure and Evolution of Online Social Networks

A preferential attachment based model is described in detail to analyze the evolution of OSNs in the presence of restrictions on node-degree that are presently being imposed in all popular OSNs.

Using Graph Concepts to Understand the Organization of Complex Systems

This tutorial demonstrates through illustrative examples, how network measures and models have contributed to the elucidation of the organization of complex systems.



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.

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.

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.

Mean-field theory for scale-free random networks

Clustering and preferential attachment in growing networks.

  • M. Newman
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
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