  We propose a simple preferential attachment model of growing network using
the complementary probability of Barab\'asi-Albert (BA) model, i.e., $\Pi(k_i)
\propto 1-\frac{k_i}{\sum_j k_j}$. In this network, new nodes are
preferentially attached to not well connected nodes. Numerical simulations, in
perfect agreement with the master equation solution, give an exponential degree
distribution. This suggests that the power law degree distribution is a
consequence of preferential attachment probability together with "rich get
richer" phenomena. We also calculate the average degree of a target node at
time t $(<k_s(t)>)$ and its fluctuations, to have a better view of the
microscopic evolution of the network, and we also compare the results with BA
model.
