Scaling Laws for Connectivity in Random Threshold Graph Models with Non-Negative Fitness Variables

摘要: We explore the scaling properties for graph connectivity in random threshold graphs. In many node limit, we provide a complete characterization existence and type of underlying zero-one laws, identify corresponding critical scalings. These results are consequences well-known facts Extreme Value Theory concerning asymptotic behavior running maxima on i.i.d. variables. important special case exponentially distributed fitness, show that (essentially unique) which ensures power-law degree distribution, does not result asymptotically almost sure (a.a.s.) sense.