  In this paper, first a theorem on the partial sum of a particular series is
given. Then, based on it, the origin of obvious simulation deviation from
theory is explained: i) why the numerically estimated \hat\gamma (degree
exponent) in [1=arXiv:cond-mat/0106096] is always smaller than \gamma (=3) that
is predicted by theory; ii) and why \hat\gamma rises monotonically as m (the
links added at each step in Barabasi-Albert (BA) model [1]) increases.
Strictly, it declares such errors are basically from the inconsistence of
simulation with the theoretical model, which is caused by an additional
incompatible condition used in simulation. In addition, noticing the evolving
differences between the initial m_0 nodes and those after, we correct the
derived BA model which unfairly omitted such differences.
