Characterizing the dynamical importance of network nodes and links.

@article{Restrepo2006CharacterizingTD,
  title={Characterizing the dynamical importance of network nodes and links.},
  author={J. Restrepo and E. Ott and B. Hunt},
  journal={Physical review letters},
  year={2006},
  volume={97 9},
  pages={
          094102
        }
}
The largest eigenvalue of the adjacency matrix of networks is a key quantity determining several important dynamical processes on complex networks. Based on this fact, we present a quantitative, objective characterization of the dynamical importance of network nodes and links in terms of their effect on the largest eigenvalue. We show how our characterization of the dynamical importance of nodes can be affected by degree-degree correlations and network community structure. We discuss how our… Expand

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References

SHOWING 1-10 OF 54 REFERENCES
The Structure and Function of Complex Networks
  • M. Newman
  • Physics, Computer Science
  • SIAM Rev.
  • 2003
TLDR
Developments in this field are reviewed, 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 processes taking place on networks. Expand
Complex networks: Structure and dynamics
Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highlyExpand
Resilience to damage of graphs with degree correlations.
  • A. Vázquez, Y. Moreno
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2003
TLDR
This work investigates the problems of site and bond percolation on graphs with degree correlations and their connection with spreading phenomena and obtains some general expressions that allow the computation of the transition thresholds or their bounds. Expand
Emergence of scaling in random networks
TLDR
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. Expand
Statistical mechanics of complex networks
TLDR
A simple model based on these two principles was able to reproduce the power-law degree distribution of real networks, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. Expand
Synchronization in large directed networks of coupled phase oscillators.
TLDR
This work studies the emergence of collective synchronization in large directed networks of heterogeneous oscillators by generalizing the classical Kuramoto model of globally coupled phase oscillators to more realistic networks and considers the case of networks with mixed positive-negative coupling strengths. Expand
Generalized percolation in random directed networks.
  • M. Boguñá, M. Serrano
  • Mathematics, Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
We develop a general theory for percolation in directed random networks with arbitrary two-point correlations and bidirectional edges--that is, edges pointing in both directions simultaneously. TheseExpand
Synchronization in networks with random interactions: theory and applications.
TLDR
Some recent results on synchronization in randomly coupled networks and applications to neuroscience, in particular, networks of Hodgkin-Huxley neurons, are included. Expand
Scale-free topology of e-mail networks.
TLDR
The resulting network exhibits a scale-free link distribution and pronounced small-world behavior, as observed in other social networks, implying that the spreading of e-mail viruses is greatly facilitated in real e- mail networks compared to random architectures. Expand
Onset of synchronization in large networks of coupled oscillators.
  • J. Restrepo, E. Ott, B. Hunt
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
TLDR
The theory of the transition from incoherence to coherence in large networks of coupled phase oscillators is studied and it is found that the theory describes the transition well in situations in which the mean-field approximation fails. Expand
...
1
2
3
4
5
...