Abstract
The threshold network model is a type of finite random graph. 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 and prove a uniform strong law of large numbers. We also prove two limit theorems for the local and global clustering coefficients.
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Ide, Y., Konno, N. & Masuda, N. Statistical Properties of a Generalized Threshold Network Model. Methodol Comput Appl Probab 12, 361–377 (2010). https://doi.org/10.1007/s11009-008-9111-5
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DOI: https://doi.org/10.1007/s11009-008-9111-5