Large Communities in a scale-free network

We prove the existence of a large complete subgraph w.h.p. in a preferential attachment random graph process with an edge-step. That is, we prove that the random graph $G_t$ produced by the so-called GLP model at time $t$ contains a complete subgraph of order $t^{\alpha }$, where $\alpha = (1-\varepsilon)\frac{1-p}{2-p}$,$\varepsilon$isanynumbersuchthat$0<\varepsilon<1$,and$0<p<1$ is a parameter of the model.