Curvature of Indoor Sensor Network: Clustering Coefficient

Abstract

Abstract We investigate the geometric properties of the communication graph in realistic low-power wireless networks. In particular, we explore the concept of the curvature of a wireless network via the clustering coefficient. Clustering coefficient analysis is a computationally simplified, semilocal approach, which nevertheless captures such a large-scale feature as congestion in the underlying network. The clustering coefficient concept is applied to three cases of indoor sensor networks, under varying thresholds on the link packet reception rate (PRR). A transition from positive curvature ("meshed" network) to negative curvature ("core concentric" network) is observed by increasing the threshold. Even though this paper deals with network curvature per se, we nevertheless expand on the underlying congestion motivation, propose several new concepts (network inertia and centroid), and finally we argue that greedy routing on a virtual positively curved network achieves load balancing on the physical network.