Somek-hop based graph metrics and noderanking in wireless sensor networks
Csaba Bíró, Gábor Kusper · Az Eszterházy Károly Tanárképző Főiskola tudományos közleményei. Tanulmányok a matematikai tudományok köréből/Az Eszterházy Károly Főiskola tudományos közleményei. Tanulmányok a matematikai tudományok köréből/Annales mathematicae et informaticae · 2019
Node localization and ranking is an essential issue in wireless sensor networks (WSNs). We model WSNs by communication graphs. In our interpretation 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, Relative Communication Graph Density), Weighted Relative Communication Graph Density, Communication Graph Redundancy, Weighted Communication Graph Redundancy. We compare them to known graph metrics, and show that they can be used for node ranking. Keywords: k-hop based graph metrics, communication graph density, com munication graph redundancy, node ranking