The detection of central nodes in complex networks is one of most challenging tasks in network theory. Many centrality measures that allow to rank nodes of the network based on their topological importance were designed. Unfortunately, most of them cannot be applied to complex networks due to their high computational complexity. This leads to the fact that simpler measures in terms of their complexity should be used or some other techniques should be designed. We propose another approach on how to detect central elements in complex networks. Instead of calculating centrality measures with a high computational complexity on complex networks, we can apply them on its smaller analogues. If the sets of central nodes in small and complex networks are similar, some centrality measures with a high computational complexity can applied to complex networks. Thus, we consider different
existing centrality measures as well as some rules from social choice theory based on majority relation (uncovered sets, untrapped sets, etc.) and different network elimination techniques. Our main focus is on the study of the similarity of sets of key nodes in complex networks and its subnetworks. The results show how the initial network should be narrowed in order to maintain a set of key nodes of the complex network and which centrality measures can be applied to complex networks. The experiments were performed on random networks with exponential degree distribution as well as on some real networks.