  In search of many social and economical systems, it is found that node
strength distribution as well as degree distribution demonstrate the behavior
of power-law with droop-head and heavy-tail. We present a new model for the
growth of weighted networks considering the connection of nodes with low
strengths. Numerical simulations indicate that this network model yields three
power-law distributions of the node degrees, node strengths and connection
weights. Particularly, the droop-head and heavy-tail effects can be reflected
in the first two ones by this new model.
