## 1 Introduction
Because of this, providing stable applications remains difficult when using the currently-existing approaches, in which only required resources (i.e., without redundancy) are assigned to a user. Reliability, even in the face of such environmental changes, is important. For that reason, we focus on a means of constructing a robust and adaptive VWSN topology for applications. To ensure robust connectivity, each node should know all routes to the other nodes. However, keeping this information up to date would require all nodes to exchange or maintain their information with each other, resulting in heavy traffic. Especially for energy-scar WSNs, strategies with low overhead are required. Therefore, we need to construct reliable VWSNs while keeping the overhead low for nodes. From the viewpoint of VWSN managers, the efficient distribution of sensor substrates is necessary in order to maximize per-sensor benefit. Therefore, a desirable VWSN construction method will be able to form as many virtual networks from the finite sensor substrates as possible and allow many users and applications to share the physical network. One solution to this type of problem is to use a hierarchical structure. Such structures offer both low overhead and high manageability because they can abstract the physical network and allow nodes to use their information in multiple applications. In our previous work, we proposed a method of construction of a VWSN topology that offers robust connectivity against node removal [13]. Our approach is inspired by brain network features, and we focus particularly on the similarity between the hierarchical modular structure of brains and the modular structure that emerges from the integration of local networks. A brain network has many structural properties, such as heavy-tailed degree distribution, rich clubs, clustering, small-world properties, hierarchical modular structure, and so on [14]. Especially, small-world properties and hierarchical modular structure contribute to the evolvability of the brain network and high communication efficiency in the global area with low metabolic cost [15]. Our conclusive goal is autonomously evolving VWSN according to the environmental changes. When congestion or event-driven burst traffic occurs or the physical topology changes according to the addition/removal/move of nodes, the resources for the virtual topology, such as time slots for the application, the number of physical paths assigned to a virtual link or new virtual links for new physical topology, should be reassigned to meet the environment. As the first step toward this goal, we introduce the structural properties of the brain network into a VWSN topology. Our approach consists of two steps: constructing modules with small-world properties and integrating the modules hierarchically. Our idea is a bottom-up design of the hierarchical structure, which is inspired by the brain. The modules in the brain network consist of sub-modules, which have a close correlation in terms of their function. In our proposed structure, a higher-tier module consists of sub-modules that are assigned to sub-applications, and the module describes an integrated system. We expect that such a modular structure taking into account modules' functions contribute to resource-efficient solutions for users' demands. However, the evaluation of resource efficiency is out of scope here. We evaluate the topology constructed by our proposal without an autonomous configuration because the performance characteristics of the constructed VWSN topology itself are primarily important. We investigate connection patterns within each module and between modules. We showed that the VWSN topology constructed by our proposal is robust against node removal on both connectivity and path length in our previous work [13]. In this paper, we show an overall architecture for constructing and running VWSN services on a VWSN topology as a further investigation of our proposed method.