Journal of Statistical Physics

, Volume 149, Issue 3, pp 505–518 | Cite as

Distinct Clusterings and Characteristic Path Lengths in Dynamic Small-World Networks with Identical Limit Degree Distribution



Many real-world networks belong to a particular class of structures, known as small-world networks, that display short distance between pair of nodes. In this paper, we introduce a simple family of growing small-world networks where both addition and deletion of edges are possible. By tuning the deletion probability q t , the model undergoes a transition from large worlds to small worlds. By making use of analytical or numerical means we determine the degree distribution, clustering coefficient and average path length of our networks. Surprisingly, we find that two similar evolving mechanisms, which provide identical degree distribution under a reciprocal scaling as t goes to infinity, can lead to quite different clustering behaviors and characteristic path lengths. It is also worth noting that Farey graphs constitute the extreme case q t ≡0 of our random construction.


Degree distribution Small world graph Complex network 



The author would like to thank the referees for the valuable suggestions and comments.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Institute for Cyber SecurityUniversity of Texas at San AntonioSan AntonioUSA

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