Many real world data and processes have a network structure and can usefully be represented as graphs. Network analysis focuses on the relations among the nodes exploring the properties of each network. We introduce a method for measuring the strength of the relationship between two nodes of a network and for their ranking. This method is applicable to all kinds of networks, including directed and weighted networks. The approach extracts dependency relations among the network's nodes from the structure in local surroundings of individual nodes. For the tasks we deal with in this article, the key technical parameter is locality. Since only the surroundings of the examined nodes are used in computations, there is no need to analyze the entire network. This allows the application of our approach in the area of large-scale networks. We present several experiments using small networks as well as large-scale artificial and real world networks. The results of the experiments show high effectiveness due to the locality of our approach and also high quality node ranking comparable to PageRank.