Structure properties of evolutionary spatially embedded networks

This work is a modeling of evolutionary networks embedded in one or two dimensional configuration space. The evolution is based on two attachments depending on degree and spatial distance. The probability for a new node n to connect with a previous node i at distance r(ni) follows ak(i)/Sigma(j)k(j) + (1 - a) r(m)(-alpha)/Sigma(j)r(nj)(-alpha), where k(i) is the degree of node i, alpha and a are tunable parameters. In spatial driven model (a = 0), the spatial distance distribution follows the power-law feature. The mean topological distance l and the clustering coefficient C exhibit phase transitions at same critical values of alpha which change with the dimensionality d of the embedding space. When a not equal 0, the degree distribution follows the "shifted power law" (SPL) which interpolates between exponential and scale-free distributions depending on the value of a. (C) 2013 Elsevier B.V. All rights reserved.