Statistical properties of a generalized threshold network model

摘要

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 withrandom weights is connected by an edge when real-valued functions of the pairof weights belong to given Borel sets. We extend several known limit theoremsfor the number of prescribed subgraphs to show that the strong law of largenumbers can be uniform convergence. We also prove two limit theorems for thelocal and global clustering coefficients.