Correlations between communicability sequence entropy and transport performance in spatially embedded networks.

We investigate electric current transport performances in spatially embedded networks with total cost restriction introduced by Li et al. [Phys. Rev. Lett. 104, 018701 (2010)10.1103/PhysRevLett.104.018701]. Precisely, the network is built from a d-dimensional regular lattice to be improved by adding long-range connections with probability P_{ij}∼r_{ij}^{-α}, where r_{ij} is the Manhattan distance between sites i and j, and α is a variable exponent, the total length of the long-range connections is restricted. In addition, each link has a local conductance given by g_{ij}∼r_{ij}^{-C}, where the exponent C is to measure the impact of long-range connections on network flow. By calculating mean effective conductance of the network for different exponent α, we find that the optimal electric current transport conditions are obtained with α_{opt}=d+1 for all C. Interestingly, the optimal transportation condition is identical to the one obtained for optimal navigation in spatially embedded networks with total cost constraint. In addition, the phenomenon can be possibly explained by the communicability sequence entropy; we find that when α=d+1, the spatial network with total cost constraint can obtain the maximum communicability sequence entropy. The results show that the transport performance is strongly correlated with the communicability sequence entropy, which can provide an effective strategy for designing a power network with high transmission efficiency, that is, the transport performance can be optimized by improving the communicability sequence entropy of the network.