  The muliplicative attribute graph (MAG) model was introduced by Kim and
Leskovec as a mathematically tractable model for networks where network
structure is believed to be shaped by features or attributes associated with
individual nodes. For large homogeneous binary MAGs, they argued through
approximation arguments that the "tail of [the] degree distribution follows a
log-normal distribution" as the number of nodes becomes unboundedly large and
the number of attributes scales logarithmically with the number of nodes. Under
the same limiting regime, we revisit the asymptotic behavior of the degree
distribution: Under weaker conditions we obtain a precise convergence result to
log-normality, develop from it reasoned log-normal approximations to the degree
distribution and derive various rates of convergence. In particular, we show
that a certain transformation of the node degree converges in distribution to a
log-normal distribution, and give its convergence rate in the form of a
Berry-Esseen type estimate.
