A generalization of the Buckley-Osthus model for web graphs

We generalize the web graph models of Buckley and Osthus (2004) and Wu et al. (2009) to a directed version in the manner of Bollobas et al. (2003) and Cooper and Frieze (2003). The graph evolution process is a mixture of five steps. The degree distribution for this general model is derived, which generalizes the results of Buckley and Osthus (2004) and of Wu et al. (2009) to a directed version. In particular, it is proved that at the critical point, the degree sequence has the form (1+O(k^-^1^/^4log^3^/^2k))C"ck^@x^2^@a^-^7^4e^-^2^k^@a.