Synchronization in Weighted Uncorrelated Complex Networks in a Noisy Environment: Optimization and Connections with Transport Efficiency
<|reference_start|>Synchronization in Weighted Uncorrelated Complex Networks in a Noisy Environment: Optimization and Connections with Transport Efficiency: Motivated by synchronization problems in noisy environments, we study the Edwards-Wilkinson process on weighted uncorrelated scale-free networks. We consider a specific form of the weights, where the strength (and the associated cost) of a link is proportional to $(k_{i}k_{j})^{\beta}$ with $k_{i}$ and $k_{j}$ being the degrees of the nodes connected by the link. Subject to the constraint that the total network cost is fixed, we find that in the mean-field approximation on uncorrelated scale-free graphs, synchronization is optimal at $\beta^{*}$$=$-1. Numerical results, based on exact numerical diagonalization of the corresponding network Laplacian, confirm the mean-field results, with small corrections to the optimal value of $\beta^{*}$. Employing our recent connections between the Edwards-Wilkinson process and resistor networks, and some well-known connections between random walks and resistor networks, we also pursue a naturally related problem of optimizing performance in queue-limited communication networks utilizing local weighted routing schemes.<|reference_end|>
@article{korniss2006synchronization,
    title={Synchronization in Weighted Uncorrelated Complex Networks in a Noisy
  Environment: Optimization and Connections with Transport Efficiency},
    author={G. Korniss},
    journal={Phys. Rev. E 75, 051121 (2007)},
    year={2006},
    doi={10.1103/PhysRevE.75.051121},
    archivePrefix={arXiv},
    eprint={cond-mat/0609098},
    primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.NI}
}