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In this paper, we study the problem of maintaining theconnectivity of a Wireless Sensor Network (WSN) using decentralisedtopology control protocols. Previous algorithms on topology controlrequire the knowledge of the density of nodes (λ) in thesensing region. However, if λ varies continuously over time,updating this information, at all nodes is impractical. Therefore,in addition to efficient maintenance of connectivity, we also wishto reduce the control overhead of the topology control algorithm.In the absence of information regarding λ we study theconnectivity properties of WSNs by means of giant components. Weshow that by maintaining the out-degree at each node as five willgive rise to a giant connected component in the network. We alsoshow that this is the smallest value that can maintain a giantconnected component irrespective of how often or by how muchλ changes.