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In this study, we investigate the effect of weight thresholding (WT) on the robustness of real-world complex networks. Here, we assess the robustness of networks after WT against various node attack strategies. We perform WT by removing a fixed fraction of weak links. The size of the largest connected component indicates the network’s robustness. We find that real-world networks subjected to WT hold a robust connectivity structure to node attack even for higher WT values. In addition, we analyze the change in the top 30% of central nodes with WT and find a positive correlation in the ranking of central nodes for weighted node centralities. Differently, binary node centralities show a lower correlation when networks are subjected to WT. This result indicates that weighted node centralities are more stable indicators of node importance in real-world networks subjected to link sparsification.

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A median (antimedian) of a profile of vertices on a graph G is a vertex that minimizes (maximizes) the remoteness value, that is, the sum of the distances to the elements in the profile. The median (or antimedian) function has as output the set of medians (antimedians) of a profile. It is one of the basic models for the location of a desirable (or obnoxious) facility in a network. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper an axiomatic characterization is obtained for the median and antimedian functions on complete graphs minus a perfect matching (also known as cocktail-party graphs). In addition a characterization of the antimedian function on complete graphs is presented.