On the robustness of configuration graphs in a random environment

The paper considers configuration graphs with vertex degrees being independent identically distributed random variables following the power-law distribution with a random parameter. The parameter of the vertex degree distribution follows the truncated gamma distribution. The authors study the robustness of such graphs to the two types of destruction processes: random and targeted. The graphs function in a random environment where the values of the vertex degree distribution parameter are chosen separately for each vertex. A comparative analysis of destruction effects on these models and on graphs with the degree distribution common for all vertices and induced by averaging over the distribution parameter has been performed. The conditions under which the study of the graphs’ behavior in a random environment can be reduced to the study of the evolution of graphs with an averaged vertex degree distribution are discussed. A comparative analysis of destruction effects of the two types of destruction processes has been performed.