Stochastic Kronecker graph revisited

Here we calculate the expected number of isolated vertices, edges, self loops and triangles in a random realization of stochastic Kronecker graph. We then establish some bounds on the values of the parameters of the stochastic Kronecker graph which are sufficient to generate large random graph with no isolated vertices, edges, self loops and triangles. Finally we show two phase transitions: one for the emergence of edges and the other for the emergence of self loops under stochastic Kronecker model of graph generation.