Characterization and control of small-world networks

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

Volumn 60, Issue 2, 1999, Pages

  Pandit, S A ^a   Amritkar, R E ^a  

^a PHYSICAL RESEARCH LABORATORY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001063412     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.R1119     Document Type: Article

References (9)

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2. J. Gaure, in Six Degrees of Separation: A Play (Vintage Books, New York, 1990).
3. D. J. Watts and S. H. Strogatz, Nature (London) 393, 440 (1998).
4. J. J. Hopfield and A. V. M. Herz, Proc. Natl. Acad. Sci. USA 92, 6655 (1995).
5. J. J. Collins and C. C. Chow, Nature (London) 393, 409 (1998).
6. From the definition of a far edge it is clear that for a far edge (Formula presented) of order (Formula presented) there does not exist a path of length (Formula presented) connecting vertices i and j. Intuitively, the absence of a path implies farness; in our definition, it means the farness of a given order μ.
7. Although we consider the spread of an epidemic, the results are equally applicable for any quantity that spreads on a network through edges, e.g., the spread of rumors, information spread in neural networks, the spread of a virus in a computer network, the spread of a disturbance in an electrical network, etc.
8. S. A. Pandit and R. E. Amritkar (unpublished).
9. As pointed out in 7, the results are applicable for any situation in which a quantity spreads on a network through edges. In some cases complete information about the network may not be known. Even in these cases the definition of far edge is useful; e.g., if only a fraction of edges are known and with this information it turns out that some edge, say (Formula presented) is not a far edge, then after adding the information about remaining edges, (Formula presented) cannot become a far edge 8.