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We study network growth from a fixed set of initially isolated nodes placedat random on the surface of a sphere. The growth mechanism we use adds edges tothe network depending on strictly local gain and cost criteria. Only nodes thatare not too far apart on the sphere may be considered for being joined by anedge. Given two such nodes, the joining occurs only if the gain of doing itsurpasses the cost. Our model is based on a multiplicative parameter lambdathat regulates, in a function of node degrees, the maximum geodesic distancethat is allowed between nodes for them to be considered for joining. For nnodes distributed uniformly on the sphere, and for lambda*sqrt(n) within limitsthat depend on cost-related parameters, we have found that our growth mechanismgives rise to power-law distributions of node degree that are invariant forconstant lambda*sqrt(n). We also study connectivity- and distance-relatedproperties of the networks.

Emergence of scale-free behavior in networks from limited-horizon linking and cost trade-offs