Maximizing Entropy Yields Spatial Scaling in Social Networks Yanqing Hu $^{1}$∗ , Yougui Wang$^{1}$, Daqing Li$^{2}$, Shlomo Havlin$^{2}$, Zengru Di $^{1}$† 1. Department of Systems Science, School of Management and Center for Complexity Research, Beijing Normal University, Beijing 100875, China 2. Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel (Dated: September 16, 2018) In addition to the well known common properties such as small world and community structures, recent empirical investigations suggest a universal scaling law for the spatial structure of social networks. It is found that the probability density distribution of an individual to have a friend at distance r scales as P ( r ) ∝ r − $^{1}$. The basic principle that yields this spatial scaling property is not yet understood. Here we propose a fundamental origin for this law based on the concept of entropy. We show that this spatial scaling law can result from maximization of information entropy, which means individuals seek to maximize the diversity of their friendships. Such spatial distribution can benefit individuals significantly in optimally collecting information in a social network. PACS numbers: 89.75.Da, 89.75.Hc, 89.65.Ef, 05.90. + m Keywords: Social Network, Spatial Structure, Information, Optimization Abstract arXiv:1002.1802v1[physics.soc-ph]9 Feb 2010 ∗ yanqing.hu.sc@gmail.com † zdi@bnu.edu.cn 1