Smallest small-world network

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 4, 2002, Pages 5-

  Nishikawa, Takashi ^a   Motter, Adilson E ^a   Lai, Ying Cheng ^a,b   Hoppensteadt, Frank C ^a,b  

^a ARIZONA STATE UNIVERSITY   (United States)

^b Arizona State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INFORMATION FLOW; REAL NETWORKS; REGULAR LATTICE; SMALL-WORLD NETWORKS;

COMPUTER SIMULATION; FAULT TOLERANT COMPUTER SYSTEMS; GENETIC ALGORITHMS; NEURAL NETWORKS; PROBABILITY;

COMPUTER NETWORKS;

ARTICLE;

EID: 41349087034     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.046139     Document Type: Article

References (16)

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2. Notions of local and global efficiency of a network were defined in V. Latora and M. Marchiori, Phys. Rev. Lett. 87, 198701 (2001) to characterize the class of small-world networks as being efficient both locally and globally. Here we use the word “efficiency” as a general term.
3. R. Albert, H. Jeong, and A.-L. Barabási, Nature (London) 401, 130 (1999).
4. D. J. Watts, Small Worlds: The Dynamics of Networks Between Order and Randomness (Princeton University Press, Princeton, 1999).
5. There are cases where other properties of the network need to be optimized at the same time. However, we believe that the average path length, whose smallness is a defining characteristic of the small-world networks, is the most significant factor in determining the efficiency of a wide class of real networks, even though the problem of optimizing more than one measure of the network was previously studied [R.F.i. Cancho and V. Solé, e-print cond-mat/0111222;
6. N. Mathias and V. Gopal, Phys. Rev. E 63, 021117 (2001)]. Moreover, other important measures of the network, such as fault tolerance and the cost of physical links are naturally optimized in our setting. The cost of physical links are bounded due to the fact that we fix the number of shortcuts.
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