Percolation analysis for constructing a robust modular topology based on a binary-dynamics model

In the context of Internet of Things, virtualization of wireless sensor networks is a crucial technology for sharing sensors as infrastructure. In our previous work, we proposed a brain-inspired method for constructing a robust and adaptive virtual wireless sensor network topology and showed that the method of constructing links between modules has crucial effect on robustness and adaptivity of the constructed virtual wireless sensor network topology. However, the best way of constructing a robust and adaptive virtual wireless sensor network topology is still unclear. Therefore, in this article, we use an analytical approach and propose a method for clarifying robustness of a topology according to the method of constructing links between modules. We add a new tool to a binary-dynamics model which is an analytical method for investigating percolation dynamics on a modular network. Evaluation by simulation showed that graphs in which the number of nodes selected as endpoint nodes of inter-module links and the degrees of the endpoint nodes before the link addition are large have robust connectivity in terms of the point of fragmentation of the network into modules when we fix the degree of the endpoint nodes after the link addition. After the point, the internal structure of modules may matter more. We additionally investigate an applicable range of our proposed method.