Possible origin of efficient navigation in small worlds

Y Hu, Y Wang, D Li, S Havlin, Z Di - Physical Review Letters, 2011 - APS
Physical Review Letters, 2011APS
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 …
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 scales as . 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.
American Physical Society
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