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D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor & Francis, London, 1991).
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Fractals and Disordered System, edited by A. Bunde, and S. Havlin (Springer, New York, 1996).
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12
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85036255694
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It follows that for scale-free networks with (Formula presented) a spanning cluster exists, even before dilution, only for (Formula presented) smaller than a certain critical threshold (Formula presented) (Formula presented) if the distribution (1) is discrete, and (Formula presented) if it is continuous). This spurious transition can be removed, for example, by imposing (Formula presented) and does not concern us here
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It follows that for scale-free networks with (Formula presented) a spanning cluster exists, even before dilution, only for (Formula presented) smaller than a certain critical threshold (Formula presented) (Formula presented) if the distribution (1) is discrete, and (Formula presented) if it is continuous). This spurious transition can be removed, for example, by imposing (Formula presented) and does not concern us here.
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14
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85036156415
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D. ben-Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, Cambridge, UK, 2000)
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D. ben-Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, Cambridge, UK, 2000).
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G.H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994)
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G.H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
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20
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85036187017
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For the case (Formula presented) (Formula presented) in Eq. (23) represents the singularity of the distribution of branch sizes. For the distribution of cluster sizes in this range one has to consider the singularity of x in Eq. (8), leading to (Formula presented) for this range
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For the case (Formula presented) (Formula presented) in Eq. (23) represents the singularity of the distribution of branch sizes. For the distribution of cluster sizes in this range one has to consider the singularity of x in Eq. (8), leading to (Formula presented) for this range.
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