Effect of network structure entropy to convergence rate of distributed synchronization algorithm in RGGs

In this paper, we firstly introduce the random geometric graph (RGG) as the model of wireless sensor networks (WSNs), and point out that the convergence rate of distributed synchronization algorithm in WSNs is depended on the second largest eigenvalue of the update matrix based on the network topology. Then we take three network structure entropies, which are degree distribution entropy, Wu entropy and SD entropy, into consideration of the convergence rate. The relationship between network structure entropy and the convergence rate is also studied. After the simulations of the three network structure entropy, we find that the degree distribution entropy is more suitable to reflect the characteristic of RGG. Finally, we verify that when the network is more regular, the degree distribution entropy will decrease and the convergence rate of the networks will hereby increase.