Representativeness in Unweighted Networks Based on Local Dependency

Structures of real-world networks show varying degrees of importance of the nodes in their surroundings. The topic of evaluating the importance of the nodes offers many different approaches. We present simple and straightforward approach for the evaluation of the nodes in undirected unweighted networks. The approach is based on x-representativeness measure which is originally intended for weighted networks. The x-representativeness takes into account the degree of the node and its nearest neighbors. Experiments with different real-world unweighted networks are presented. To apply the presented method it is necessary to transform undirected unweighted network into weighted network. Weights in our experiments are measured by dependency between adjacent nodes. The aim of these experiments is to show that the x-representativeness can be used to deterministically reduce the unweighted network to differently sized samples of representatives, while maintaining topological properties of the original network.