  The threshold network model is a type of finite random graphs. In this paper,
we introduce a generalized threshold network model. A pair of vertices with
random weights is connected by an edge when real-valued functions of the pair
of weights belong to given Borel sets. We extend several known limit theorems
for the number of prescribed subgraphs to show that the strong law of large
numbers can be uniform convergence. We also prove two limit theorems for the
local and global clustering coefficients.
