@article{Leri_Pavlov_2017, title={Random Graphs’ Robustness in Random Environment}, volume={46}, url={https://ajs.or.at/index.php/ajs/article/view/vol46-3-4-9}, DOI={10.17713/ajs.v46i3-4.674}, abstractNote={We consider configuration graphs the vertex degrees of which are independent and<br />  follow the power-law distribution. Random graphs dynamics takes place in a random<br />  environment with the parameter of vertex degree distribution following<br />  uniform distributions on finite fixed intervals. As the number of vertices tends<br />  to infinity the limit distributions of the maximum vertex degree and the number<br />  of vertices with a given degree were obtained. By computer simulations we study<br />  the robustness of those graphs from the viewpoints of link saving and node survival<br />  in the two cases of the destruction process: the ``targeted attack’’ and the<br />  ``random breakdown’’. We obtained and compared the results under the conditions that<br />  the vertex degree distribution was averaged with respect to the distribution of the<br />  power-law parameter or that the values of the parameter were drawn from the uniform<br />  distribution separately for each vertex.}, number={3-4}, journal={Austrian Journal of Statistics}, author={Leri, Marina and Pavlov, Yury}, year={2017}, month={Apr.}, pages={89–98} }