• 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}
}
• Published 10 March 2011
• Mathematics
• ArXiv
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, Mathematics
ArXiv
• 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 Science
IEEE 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

• Guoqiang Mao
• Computer Science
2012 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 Science
ArXiv
• 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 Science
2012 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.

## References

SHOWING 1-10 OF 20 REFERENCES

### Impact of interferences on connectivity in ad hoc networks

• Computer Science
IEEE/ACM Transactions on Networking
• 2005
It is proved that if /spl gamma/ is nonzero but small enough, there exist node spatial densities for which the network contains a large (theoretically infinite) cluster of nodes, enabling distant nodes to communicate in multiple hops.

### Connectivity of random k-nearest-neighbour graphs

• Mathematics, Computer Science
• 2005
This paper improves lower and upper bounds to 0.3043 log n and 0.5139 log n, respectively, of the threshold for connectivity of a random geometric graph, and proves that if k ≤ 0.7209 log n then the probability that these discs cover S n tends to 0 as n → ∞ while, if k ≥ 0.9967log n, then the likelihood that the discs covered by these discs tends to 1 as n→ ∞.

### On the Connectivity of Ad Hoc Networks

This paper presents a framework for the calculation of stochastic connectivity properties of wireless multihop networks, and compute a tight approximation for the critical (r0 ,n )pairs that are required to keep the network connected with a probability close to one.

### Closing the Gap in the Capacity of Wireless Networks Via Percolation Theory

• Computer Science
IEEE Transactions on Information Theory
• 2007
An achievable bit rate per source-destination pair in a wireless network of n randomly located nodes is determined adopting the scaling limit approach of statistical physics. It is shown that

### Extremal properties of three-dimensional sensor networks with applications

This work investigates the network topology according to the region of deployment, the number of deployed sensors, and their transmitting/sensing ranges, and shows how these results affect algorithmic aspects of the network by designing specific distributed protocols for sensor networks.

### The Number of Neighbors Needed for Connectivity of Wireless Networks

• Computer Science
Wirel. Networks
• 2004
It is shown that in a network with n randomly placed nodes, each node should be connected to Θ(log n) nearest neighbors, and it appears that the critical constant may be close to one, but that remains an open problem.

### On the minimum node degree and connectivity of a wireless multihop network

This paper derives an analytical expression that enables the determination of the required range r0 that creates, for a given node density ρ, an almost surely k--connected network and investigates two fundamental characteristics of a wireless multi -hop network: its minimum node degree and its k--connectivity.

### A Strong Law for the Longest Edge of the Minimal Spanning Tree

Suppose X 1 , X 2 , X are independent random points in Rd, d > 2, with common density f, having connected compact support Ω with smooth boundary ∂Ω, with f|Ω continuous. Let M n denote the smallest r

### Connectivity and Latency in Large-Scale Wireless Networks with Unreliable Links

• Computer Science
IEEE INFOCOM 2008 - The 27th Conference on Computer Communications
• 2008
It is shown that due to the dynamic behavior of links, a delay is incurred for any transmission even when propagation delay is ignored, and the delay scales linearly with the Euclidean distance between the sender and the receiver when the network is in the subcritical phase.

### Asymptotic critical transmission radius and critical neighbor number for k-connectivity in wireless ad hoc networks

• Mathematics
MobiHoc '04
• 2004
This paper provides a precise asymptotic distribution of the critical transmission radius for k-connectivity and an improve asymPTotic almost sure upper bound on the critical neighbor number for k.connectivity in a wireless ad hoc network whose nodes are uniformly an independently distribute in a unit-area square or disk.