Rigorous results on the threshold network model
  We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the vertex degree, degree correlation, and the number of prescribed subgraphs. We also generalize some results in the spatially extended cases. 
Norio Konno, Naoki Masuda, Rahul Roy, Anish Sarkar