A novel wireless sensor network topology with fewer links

This paper, based on k-NN graph, presents symmetric (k, j)-NN graph (1 ≤ j < k), a brand new topology which could be adopted by a series of network-based structures. We show that the k nearest neighbors of a node exert disparate influence on guaranteeing network connectivity, and connections with the farthest j ones among these k neighbors are competent to build up a connected network, contrast to the current popular strategy of connecting all these k neighbors. In particular, for a network with node amount n up to 10, as experiments demonstrate, connecting with the farthest three, rather than all, of the five nearest neighbor nodes, i.e. (k, j) = (5, 3), can guarantee the network connectivity in high probabilities. We further reveal that more than 0.75n links or edges in 5-NN graph are not necessary for the connectivity. Moreover, a composite topology combining symmetric (k, j)-NN and random geometric graph (RGG) is constructed for constrained transmission radii in wireless sensor networks (WSNs) application.