2006/07/31 by Steffen Bohn, Marcelo O. Magnasco · 5 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevlett.98.088702
4 pages, 3 figures
arxiv created 2006/07/31 · openalex publication_date 2007/02/21 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
The structure and properties of optimal networks depend on the cost functional being minimized and on constraints to which the minimization is subject. We show here two different formulations that lead to identical results: minimizing the dissipation rate of an electrical network under a global constraint is equivalent to the minimization of a power-law cost function introduced by Banavar et al. [Phys. Rev. Lett. 84, 4745 (2000)10.1103/PhysRevLett.84.4745]. An explicit scaling relation between the currents and the corresponding conductances is derived, proving the potential flow nature of the latter. Varying a unique parameter, the topology of the optimized networks shows a transition from a tree topology to a very redundant structure with loops; the transition corresponds to a discontinuity in the slope of the power dissipation.