When a fraction of nodes, , is removed randomly from an ER network of degree , there exists a critical threshold, . Above there exists a giant component (largest cluster) of size, . fulfills, . For the solution of this equation is , i.e., there is no giant component.

At , the distribution of cluster sizes behaves as a power law, ~ which is a feature of phase transition.

Alternatively, if one adds randomly selected edges one at a time, starting with

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