# 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…

## 5 Citations

### Connectivity of Large Scale Networks: Distribution of Isolated Nodes

- Computer Science, MathematicsArXiv
- 2011

This study provides the asymptotic distribution of the number of isolated nodes in random networks with nodes Poissonly distributed on a unit square under a generic random connection model.

### Connectivity of Large-Scale CSMA Networks

- Computer ScienceIEEE Transactions on Wireless Communications
- 2012

It is shown that the transmission power only needs to be increased by a constant factor to combat interference and maintain connectivity compared with that considering a unit disk model (UDM) without interference.

### Research on wireless multi-hop networks: Current state and challenges

- Computer Science2012 International Conference on Computing, Networking and Communications (ICNC)
- 2012

Recent development in wireless multi-hop networks is briefly overview and research challenges and opportunities in the area are discussed, with a focus on the network connectivity.

### Connectivity of Confined Dense Networks: Boundary Effects and Scaling Laws

- Computer ScienceArXiv
- 2012

The probability that a dense network confined within a given geometry is fully connected is studied, using a cluster expansion approach often used in statistical physics to analyze the effects that the boundaries of the geometry have on connectivity.

### On the quality of wireless network connectivity

- Computer Science2012 IEEE Global Communications Conference (GLOBECOM)
- 2012

It is shown that the largest eigenvalue of the probabilistic connectivity matrix can serve as a good measure of the quality of network connectivity.

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