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We study evolving networks where new nodes when attached to the network form links with other nodes of preferred distances. A particular case is where always the shortest distances are selected ("make friends with the friends of your present friends"). We present simulation results for network parameters like the first eigenvalue of the graph Laplacian (synchronizability), clustering coefficients, average distances, and degree distributions for different distance preferences and compare withdoi:10.1103/physreve.66.036126 pmid:12366203 fatcat:c57vbv2v5bfrjlcljiw3sxg7i4