Network robustness and graph topology
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The study of robustness and connectivity properties are important in the analysis of complex networks. This paper reports on an effort to compare different network topologies according to their algebraic connectivity, network criticality, average node degree, and average node betweenness. We consider different network types and study the behavior of these various metrics as scale is increased. Based on extensive simulations, we suggest some guidelines for the design and simplification of networks. The main finding is that, algebraic connectivity, network criticality, average degree, and average node betweenness capture different properties of a graph. Depending on the nature of the problem at hand, one needs to select which one is appropriate to use as the main metric for network analysis.