Random Graphs' Robustness in Random Environment
AbstractWe consider configuration graphs the vertex degrees of which are independent and
follow the power-law distribution. Random graphs dynamics takes place in a random
environment with the parameter of vertex degree distribution following
uniform distributions on finite fixed intervals. As the number of vertices tends
to infinity the limit distributions of the maximum vertex degree and the number
of vertices with a given degree were obtained. By computer simulations we study
the robustness of those graphs from the viewpoints of link saving and node survival
in the two cases of the destruction process: the ``targeted attack'' and the
``random breakdown''. We obtained and compared the results under the conditions that
the vertex degree distribution was averaged with respect to the distribution of the
power-law parameter or that the values of the parameter were drawn from the uniform
distribution separately for each vertex.
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