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term evolution from the initial uniform distribution (each node modify the neighborhood more than 40000 times), the system achieves its stationary state (Fig. 3e). The maximum entropy is 7.15 and the corresponding PDF of the distance between the friends scales as P ( r ) ∝ r − 1 (Fig. 3d and supplementary IIIB), which are very close to the results obtained by OM. So we conclude that P ( r ) ∝ r − 1 is the optimal PDF of distances of friendships for collecting maximal information. It implies that, the spatial structure of the real social networks is the most optimal structure which leads to the maximum diversity of the friends’ location and can help individuals to collect infor- mation e ffi ciently. We note that, it can be proved analytically, under the assumption that the energy 

