Network boundary recognition via graph-theory

Wireless sensor networks (WSNs) are considered an adequate solutions for environmental monitoring and surveillance applications, where the physical presence of humans is impossible or costly. In the next future, it is foreseen that nodes will be part of a localization system, that will be able to estimate their locations, aiding the coordination for the most consuming activities such as relaying and routing. However, in some particular conditions, it is useful to know only logical information about the node locations and, specifically it would be sufficient to know if they are in the inner part or at the boundary of the network. In this paper we propose a technique for the identification of nodes at the network boundary, based solely on connectivity information, assumed to be available at a central unit The algorithm is a useful network management tool as it allows one (the central unit) to detect the formation or existence of topological holes, enabling corrective measures such as redeployment in affected areas or warning dead-end nodes of their condition. Since connectivity information is learned overtime by the network sinks (and the coordinator to which they are connected to), the proposed network boundary discovery algorithm incurs no additional cost to the network at steady state of operation. The algorithm is based on a spectral graph clusterization technique, which first tessellates the network in small cells that circumvent (eventual) connectivity holes. Then, the border nodes of each cluster are identified using beetweness centrality scores and clusters are classified by their adjacencies. Since nodes located simultaneously at the boundary of adjacent clusters are obviously not at the border of a hole, the procedure allows the identification of nodes that are exclusively at the boundary of one cluster, ultimately yielding the collection of nodes at the boundaries of the network in general.