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Complex Networks by Shlomo Havlin, Reuven Cohen

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10   Percolation on complex networks

10.1 Introduction

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It is well known [BH96, SA94] that in grids and other organized lattices, in any dimension larger than one, a percolation phase transition occurs. The usual percolation model assumes that the sites (nodes) or bonds (links) in the lattice are occupied with some probability (or density), p, and unoccupied with probability q= 1 − p. The system is considered percolating if there is a path from one side of the lattice to the other, passing only through occupied links and nodes. When such a path exists, the component or cluster of sites that spans the network from side to side is called the spanning ...

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