Growing spatial scale-free graphs by selecting local edges

A simple model of spatial scale-free graph is suggested for the growing Internet structure where new vertices pop-up at randomly located positions and their connections to the growing graph are determined by local factors. The strength distribution is observed to have non-trivial degree dependence. The same model without the underlying Euclidean space gives a much simpler route to Barab\'asi-Albert model where numerical effort grows linearly with $N$.