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 a k i  j k j + (1 − a) r −α ni  j r −α nj , where k i is the degree of node i, α 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 α which change with the dimensionality d of the embedding space. When a ̸ = 0, the degree distribution follows the ''shifted power law'' (SPL) which interpolates between exponential and scale-free distributions depending on the value of a.