• Corpus ID: 31656930

Connectivity of Large Scale Networks: Emergence of Unique Unbounded Component

@article{Mao2011ConnectivityOL,
  title={Connectivity of Large Scale Networks: Emergence of Unique Unbounded Component},
  author={Guoqiang Mao and Brian. D. O. Anderson},
  journal={ArXiv},
  year={2011},
  volume={abs/1103.1991}
}
This paper studies networks where all nodes are distributed on a unit square $A\triangleq[(-1/2,1/2)^{2}$ following a Poisson distribution with known density $\rho$ and a pair of nodes separated by an Euclidean distance $x$ are directly connected with probability $g(\frac{x}{r_{\rho}})$, independent of the event that any other pair of nodes are directly connected. Here $g:[0,\infty)\rightarrow[0,1]$ satisfies the conditions of rotational invariance, non-increasing monotonicity, integral… 

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