Small-world effect in a uniform-radius broadcasting network

Authors

  • Gerold Pedemonte ⋅ PH National Institute of Physics, University of the Philippines Diliman
  • May Lim ⋅ PH National Institute of Physics, University of the Philippines Diliman

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, βc, equivalent to the percolation threshold of the system, that marks a transition in network characteristics.  For β < βc, the network exhibits Poisson properties that are also found in Erdos-Renyi networks, and is consistent with the random geometric network model, G(N, r), for small values of r. For βc < β < 1, the network exhibits the small-world property
of 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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Issue

Article ID

SPP2012-4B-4

Section

Complex Systems

Published

2012-10-22

How to Cite

[1]
G Pedemonte and M Lim, Small-world effect in a uniform-radius broadcasting network, Proceedings of the Samahang Pisika ng Pilipinas 30, SPP2012-4B-4 (2012). URL: https://proceedings.spp-online.org/article/view/SPP2012-4B-4.