Abstract: Random graphs are matrices with independent 0–1 elements with probabilities determined by a small number of parameters. One of the oldest models is the Rasch model where the odds are ratios of positive numbers scaling the rows and columns. Later Persi Diaconis with his coworkers rediscovered the model for symmetric matrices and called the model beta. Here we give goodness-of-fit tests for the model and extend the model to a version of the block model introduced by Holland, Laskey and Leinhard.
Keywords: random graph; maximum likelihood; rank entropy
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Csiszár, V.; Hussami, P.; Komlós, J.; Móri, T.F.; Rejtõ, L.; Tusnády, G. Testing Goodness of Fit of Random Graph Models. Algorithms 2012, 5, 629-635.
Csiszár V, Hussami P, Komlós J, Móri TF, Rejtõ L, Tusnády G. Testing Goodness of Fit of Random Graph Models. Algorithms. 2012; 5(4):629-635.
Csiszár, Villõ; Hussami, Péter; Komlós, János; Móri, Tamás F.; Rejtõ, Lídia; Tusnády, Gábor. 2012. "Testing Goodness of Fit of Random Graph Models." Algorithms 5, no. 4: 629-635.