Random Graph Models with Non-Independent Edges

Zohre Ranjbar Mojaveri
2020 Current Trends in Computer Sciences & Applications  
Random graph models play an important role in describing networks with random structural features. The most classical model with the largest number of existing results is the Erd˝os-R´enyi random graph, in which the edges are chosen interdependently at random, with the same probability. In many real-life situations, however, the independence assumption is not realistic. We consider random graphs in which the edges are allowed to be dependent. In our model the edge dependence is quite general,
more » ... is quite general, we call it p-robust random graph. Our main result is that for any monotone graph property, the p-robust random graph has at least as high probability to have the property as an Erd˝os-R´enyi random graph with edge probability p. This is very useful, as it allows the adaptation of many results from Erd˝os-R´enyi random graphs to a non-independent setting, as lower bounds.
doi:10.32474/ctcsa.2020.02.000130 fatcat:gfj76vnqdnf63nkqlfjup3hm2a