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Characterization of a Connectivity Measure for Sparse Wireless Multi-hop Networks
Srinath Perur and Sridhar Iyer

The extent to which a wireless multi-hop network is connected is usually measured by the probability that all the nodes form a single connected component. This measure is called connectivity. We find this unsuitable for use with sparse networks since it is not indicative of the actual communication capability of the network, and can be unresponsive to changes in network parameters. We propose an alternative measure called reachability, defined as the fraction of node pairs in the network that are connected. We claim that it is more intuitive and expressive than connectivity when dealing with sparse networks. We obtain analytical expressions for reachability for two and three nodes in the static case. We identify reachability as growing according to the logistic growth model and present a regression model for reachability in terms of number of nodes and normalized transmission range. This model is applicable for static networks with up to 500 nodes. We also extend this model to larger networks using an approximation. These characterizations of reachability can be used by a network designer to estimate the trade off between how connected the network is, the number of nodes, the area of operation, and transmission range of nodes.

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