# Small-world effect in a uniform-radius broadcasting network

## Abstract

We studied the properties of a network formed from nodes that are randomly deployed over an *L × L *area. All nodes are broadcasting at a uniform transmission radius,* βL . *Connections are established when nodes are within their respective communication ranges. We found a critical value, β

_{c}, equivalent to the percolation threshold of the system, that marks a transition in network characteristics. For

*β < β*, the network exhibits Poisson properties that are also found in Erdos-Renyi networks, and is consistent with the random geometric network model,

_{c}*G(N, r)*, for small values of

*r*. For

*β*, the network exhibits the small-world property

_{c}< β < 1of high average clustering coefficient in conjunction with low average shortest path length. For

*β > 1*, we obtained a regular network where each node is connected to all other nodes in the network. We also show a fitting function for the mean degree, 〈

*k*〉, as a function of

*β*which captures the quadratic dependence of 〈

*k*〉 for small

*β*. We offer an explanation why such a transition occurs in the context of percolation and use the results for optimal communication operation in broadcasting systems.

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## Published

## How to Cite

*Proceedings of the Samahang Pisika ng Pilipinas*

**30**, SPP2012-4B-4 (2012). URL: https://proceedings.spp-online.org/article/view/SPP2012-4B-4.