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Rate Equation Approach for Growing Networks

  • P.L. Krapivsky
  • S. Redner
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 625)

Abstract

The rate equations are applied to investigate the structure of growing networks. Within this framework, the degree distribution of a network in which nodes are introduced sequentially and attach to an earlier node of degree k with rate A k ˜kγ is computed. Very different behaviors arise for γ < 1, γ = 1 and γ > 1. The rate equation approach is extended to determine the joint order-degree distribution, the degree correlations of neighboring nodes, as well as basic global properties. The complete solution for the degree distribution of a finite-size network is outlined. Some unusual properties associated with the most popular node are discussed; these follow simply from the order-degree distribution. Finally, a toy protein interaction network model is investigated, where the network grows by the processes of node duplication and particular form of random mutations. This system exhibits an infinite-order percolation transition, giant sample-specific fluctuations, and a non-universal degree distribution.

Keywords

Degree Distribution Node Degree Complete Bipartite Graph Degree Correlation Giant Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  • P.L. Krapivsky
    • 1
  • S. Redner
    • 1
  1. 1.Center for BioDynamics, Center for Polymer Studies and Department of PhysicsBoston UniversityBostonUSA

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