Quasi scale-free geographically embedded networks over DLA-generated aggregates

This paper proposes a novel model to construct quasi scale-free geographically-embedded networks, in which the network’s nodes have been generated by means of a Diffusion Limited Aggregation (DLA) process, and the links connecting a new node i to others are generated using a link radiusRli based on the Euclidean distance. The network is constructed by means of an evolutionary-based algorithm, aiming at minimizing the error between the actual degree distribution of the network under construction and that of the scale free networks, k−γ. Several algorithms for generating scale-free geographically-embedded networks over regular Euclidean lattices can be found in the literature but, to the best of our knowledge, the general case over complex or fractal substrates had not been tackled up until now. Although well-known in very large complex networks (with a huge number of nodes and links), the scale-free property has received much less attention for small geographically-embedded networks, in which the study of networks’ properties is much more difficult. The idea of this work is to evolve the link radii for all the nodes in the network, aiming at finally fulfilling the scale-free property, if possible. Our experimental work shows that the proposed model is actually able to generate quasi scale-free geographically embedded networks in an efficient way. Discussions on the algorithm’s performance to generate scale-free networks, a special encoding to improve the search, and the algorithm’s computational evolution are given in the paper. Alternative possibilities of distribution objective (such as Poissonian, which leads to random geographically-embedded networks) are also tested and discussed in this work.