Universality and non-universality in behavior of self-repairing random networks
We numerically study one-parameter family of random single-cluster systems. A finite-concentration topological phase transition from the net-like to the tree-like phase (the latter is without a backbone) is present in all models of the class. Correlation radius index νB of the backbone in the net-like phase; graph dimensions—dmin of the tree-like phase, and Dmin of the backbone in the net-like phase appear to be universal within the accuracy of our calculations, while the backbone fractal dimension DB is not universal: it depends on the parameter of a model.
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