scales linearly with system size, i.e. w = cL , for L → $^{+}$∞ , that P ( r ) ∝ r − 1 will be the optimal distribution for maximizing entropy among all power law distributions (see supplementary IIC for detailed analysis ). 

## III. CONCLUSION 

From the empirical results, we conclude that the probability distribution of having a friend at distance r scales as P ( r ) ∝ r − 1 which is a universal spatial property for social networks. It is shown here that the origin of this spatial scaling law may result from the maximization of entropy which can benefit individuals for optimally collecting info rmation. 

Acknowledgement. We thank Dr. R. Lambiotte for providing us the mobile network data at the beginning of this research. Yanqing Hu wishes to thank Prof. Fukang Fang, Prof. Gang Hu, Dr. Jiang Zhang, Dr. Erbo Zhaofor and Dr. Yiming Ding for very useful discussions. The work is par- tially supported by NSFC under Grant No. 70974084, No. 60534080 and No. 70771011. Daqing Li and Shlomo Havlin thank the ONR, EU project Epiwork and the Israel Science Foundation for financial support. 

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