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The small-world phenomenon is one of the most important properties found
in social networks. It includes both short path lengths and efficient
navigation between two individuals. It is found by Kleinberg that
navigation is efficient only if the probability density distribution of
an individual to have a friend at distance r scales as P(r) ~ r-1. Although this spatial scaling is found in many empirical
studies, the origin of how this scaling emerges is still missing. In
this letter, we propose the origin of this scaling law using the concept
of entropy from statistical physics and show that this scaling is the
result of optimization of collecting information in social networks.
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