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Optimizing Synchronization, Flow, and Robustness in Weighted Complex Networks

In: Handbook of Optimization in Complex Networks

Author

Listed:
  • G. Korniss

    (Rensselaer Polytechnic Institute)

  • R. Huang

    (Rensselaer Polytechnic Institute)

  • S. Sreenivasan

    (Rensselaer Polytechnic Institute
    Rensselaer Polytechnic Institute)

  • B. K. Szymanski

    (Rensselaer Polytechnic Institute)

Abstract

Complex biological, social, and technological systems can be often modeled by weighted networks. The network topology, together with the distribution of available link or node capacity (represented by weights) and subject to cost constraints, strongly affect the dynamics or performance of the networks. Here, we investigate optimization in fundamental synchronization and flow problems where the weights are proportional to (k i k j )β with k i and k j being the degrees of the nodes connected by the edge. In the context of synchronization, these weights represent the allocation of limited resources (coupling strength), while in the associated random walk and current flow problems, they control the extent of hub avoidance, relevant in routing and search. In this chapter, we review fundamental connections between stochastic synchronization, random walks, and current flow, and we discuss optimization problems for these processes in the above weighted networks.

Suggested Citation

  • G. Korniss & R. Huang & S. Sreenivasan & B. K. Szymanski, 2012. "Optimizing Synchronization, Flow, and Robustness in Weighted Complex Networks," Springer Optimization and Its Applications, in: My T. Thai & Panos M. Pardalos (ed.), Handbook of Optimization in Complex Networks, chapter 0, pages 61-96, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0857-4_3
    DOI: 10.1007/978-1-4614-0857-4_3
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    Cited by:

    1. Stefano Martinazzi & Andrea Flori, 2020. "The evolving topology of the Lightning Network: Centralization, efficiency, robustness, synchronization, and anonymity," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-18, January.

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