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The internal organization of complex networks often has striking consequenceson either their response to external perturbations or on their dynamicalproperties. In addition to small-world and scale-free properties, clustering isthe most common topological characteristic observed in many real networkedsystems. In this paper, we report an extensive numerical study on the effectsof clustering on the structural properties of complex networks. Strongclustering in heterogeneous networks induces the emergence of a core-peripheryorganization that has a critical effect on the percolation properties of thenetworks. We observe a novel double phase transition with an intermediate phasein which only the core of the network is percolated and a final phase in whichthe periphery percolates regardless of the core. This result implies breakingof the same symmetry at two different values of the control parameter, in starkcontrast to the modern theory of continuous phase transitions. Inspired by thiscore-periphery organization, we introduce a simple model that allows us toanalytically prove that such an anomalous phase transition is in fact possible.

Double percolation phase transition in clustered complex networks