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Geographic routing in social networks.
David Liben-Nowell1, Jasmine Novak, Ravi Kumar
1Department of Mathematics and Computer Science, Carleton College, 1 North College Street, Northfield, MN 55057, USA. dlibenno@carleton.edu
Summary
Social networks exhibit a "small world" phenomenon, where people are connected by short chains of friends. This study introduces a new model explaining how geography influences friendships, revealing that short chains are discoverable in networks with this relationship.
Area of Science:
- Social network analysis
- Network science
- Sociology
Background:
- The
- small world
- phenomenon describes short average path lengths between nodes in large networks.
- Existing theoretical models for social networks do not fully capture real-world behavior.
- The role of geography in social network formation requires further investigation.
Purpose of the Study:
- To develop and validate a new theoretical model for social network formation that incorporates geographical factors.
- To analyze the relationship between geography and friendship probability in large-scale social networks.
- To demonstrate the analytical discoverability of short chains in networks exhibiting the proposed geographical relationship.
Main Methods:
- Introduction of a novel social network model where friendship probability is inversely proportional to the number of closer individuals.
- Empirical analysis of a large social network to quantify the proportion of geography-independent and geography-dependent friendships.
- Analytical proof of the existence and discoverability of short chains in networks adhering to the proposed geographical relationship.
Main Results:
- Approximately one-third of friendships in the analyzed large social network are independent of geographical proximity.
- The remaining two-thirds of friendships exhibit a relationship consistent with the proposed model, where proximity influences connection probability.
- Analytical findings confirm that short chains are discoverable in all networks demonstrating the geographical friendship relationship.
Conclusions:
- Geography plays a significant role in shaping social network structures, influencing a substantial portion of friendships.
- The proposed model provides a more accurate representation of real-world social network dynamics than previous theoretical approaches.
- The inherent structure of networks with geographical influence guarantees the existence and discoverability of short social chains.