Somek-hop based graph metrics and noderanking in wireless sensor networks

Abstract

Node localization and ranking is an essential issue in wireless sensor networks (WSNs). We model WSNs by communication graphs. In our inter-pretation a communication graph can be directed, in case of heterogeneous sensor nodes, or undirected, in case of homogeneous sensor nodes, and must be strongly connected. There are many metrics to characterize networks, most of them are either global ones or local ones. The local ones consider only the immediate neighbors of the observed nodes. We are not aware of a metric which considers a subgraph, i.e., which is between global and local ones. So our main goal was to construct metrics that interpret the local properties of the nodes in a wider environment. For example, how dense the environment of the given node, or in which extent it can be relieved within its environment. In this article we introduce several novel 𝑘 -hop based density and redundancy metrics: Weighted Communication Graph Density ( 𝒲𝒞𝒢𝒟 ), Relative Communication Graph Density ( ℛ𝒞𝒢𝒟 ), Weighted Relative Communication Graph Density ( 𝒲ℛ𝒞𝒢𝒟 ), Communication Graph Redundancy ( 𝒞𝒢ℛ ), Weighted Communication Graph Redundancy ( 𝒲𝒞𝒢ℛ ). We compare them to known graph metrics, and show that they can be used for node ranking.