### Random Graphs' Robustness in Random Environment

#### Abstract

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.

#### Full Text:

PDF#### References

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DOI: http://dx.doi.org/10.17713/ajs.v46i3-4.674

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