  We theoretically and numerically investigated the threshold network model
with a generic weight function where there were a large number of nodes and a
high threshold. Our analysis was based on extreme value theory, which gave us a
theoretical understanding of the distribution of independent and identically
distributed random variables within a sufficiently high range. Specifically,
the distribution could be generally expressed by a generalized Pareto
distribution, which enabled us to formulate the generic weight distribution
function. By using the theorem, we obtained the exact expressions of degree
distribution and clustering coefficient which behaved as universal power laws
within certain ranges of degrees. We also compared the theoretical predictions
with numerical results and found that they were extremely consistent.
