This paper is concerned with distributed detection of central nodes in complex networks using closeness centrality. Closeness centrality plays an essential role in network analysis. Evaluating closeness centrality exactly requires complete knowledge of the network; for large networks, this may be inefficient, so closeness centrality should be approximated. Distributed tasks such as leader election can make effective use of centrality information for highly central nodes, but complete network information is not locally available. This paper refines a distributed centrality computation algorithm by You et al.  by pruning nodes which are almost certainly not most central. For example, in a large network, leave nodes can not play a central role. This leads to a reduction in the number of messages exchanged to determine the centrality of the remaining nodes. Our results show that our approach reduces the number of messages for networks which contain many prunable nodes. Our results also show that reducing the number of messages may have a positive impact on running time and memory size.