This paper discusses the degree distribution of a type of social networks and some technological networks with similar topological structures. Firstly, we propose a most simplified model and try to show analytically that the degree distribution and the act degree distribution are well consistent, but the distribution of the number of the nodes inside an act have much smaller influence on the degree distribution. Secondly, we perform numerical simulations in a more general situation of the model, so as to show that the above mentioned conclusion is rather universal. This model leads to a conclusion that these generalized collaboration networks usually have a degree distribution between the power law and the exponential function. In the last part of the article, we introduce very briefly the results of the empirical statistical investigation on some practical collaboration networks to show that the model is valid for generalized collaboration networks.