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Phys. Rev. E 69, 026108 (2004) [5 pages]

Growing networks with geographical attachment preference: Emergence of small worlds

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Jonathan Ozik1,*, Brian R. Hunt2, and Edward Ott3
1Department of Physics and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
2Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
3Department of Physics, Department of Electrical and Computer Engineering, and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA

Received 30 July 2003; published 23 February 2004

We introduce a simple mechanism for the evolution of small world networks. Our model is a growing network in which all connections are made locally to geographically nearby sites. Although connections are made purely locally, network growth leads to stretching of old connections and to high clustering. Our results suggest that the abundance of small world networks in geographically constrained systems is a natural consequence of system growth and local interactions.

© 2004 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.69.026108
DOI:
10.1103/PhysRevE.69.026108
PACS:
02.50.Cw, 05.10.-a, 89.75.-k, 05.45.Pq

*Electronic address: jozik@umd.edu

 
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