Exactly solvable small-world network

@article{Dorogovtsev2000ExactlySS,
  title={Exactly solvable small-world network},
  author={Sergey N. Dorogovtsev and Jos{\'e} F. F. Mendes},
  journal={EPL},
  year={2000},
  volume={50},
  pages={1-7}
}
We present an exact description of a crossover between two different regimes of simple small-world networks. Each of the sites chosen with a probability p from n sites of an ordered system defined on a circle is connected to all other sites selected in such a way. Every link is of a unit length. While p changes from 0 to 1, an averaged shortest distance between a pair of sites changes from ~ n to = 1. We find the distribution of the shortest distances P(l) and obtain a scaling form of (p,n). In… Expand

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