The analysis of networks affects the research of many real phenomena. The complex network structure can be viewed as a network's state at the time of the analysis or as a result of the process through which the network arises. Research activities focus on both and, thanks to them, we know not only many measurable properties of networks but also the essence of some phenomena that occur during the evolution of networks. One typical research area is the analysis of co-authorship networks and their evolution. In our paper, the analysis of one real-world co-authorship network and inspiration from existing models form the basis of the hypothesis from which we derive new 3-lambda network model. This hypothesis works with the assumption that regular behavior of nodes revolves around an average. However, some anomalies may occur. The 3-lambda model is stochastic and uses the three parameters associated with the average behavior of the nodes. The growth of the network based on this model assumes that one step of the growth is an interaction in which both new and existing nodes are participating. In the paper we present the results of the analysis of a co-authorship network and formulate a hypothesis and a model based on this hypothesis. Later in the paper, we examine the outputs from the network generator based on the 3-lambda model and show that generated networks have characteristics known from the environment of real-world networks.