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Generally, the threshold of percolation in complex networks depends on theunderlying structural characterization. However, what topological propertyplays a predominant role is still unknown, despite the speculation of someauthors that degree distribution is a key ingredient. The purpose of this paperis to show that power-law degree distribution itself is not sufficient tocharacterize the threshold of bond percolation in scale-free networks. Toachieve this goal, we first propose a family of scale-free networks with thesame degree sequence and obtain by analytical or numerical means severaltopological features of the networks. Then, by making use of therenormalization group technique we determine the threshold of bond percolationin our networks. We find an existence of non-zero thresholds and demonstratethat these thresholds can be quite different, which implies that power-lawdegree distribution does not suffice to characterize the percolation thresholdin scale-free networks.

Different thresholds of bond percolation in scale-free networks with identical degree sequence