Three sets of data in the pajek program were taken as an example,with different data densities and sizes. The Markov random graph model and two exponential random graph models based on Snijders's new specification were used to make comparative analysis on the three sets of data.The results show that the decay problem occurs in the Markov random graph model and that the degradation becomes more serious with increasing size and density of the network.The results also indicate that the exponential random models have higher goodness of fit compared with the Markov random model,therefore,the Markov random model can be replaced by the improved exponential random model.