Simulation and measurement of a two-stage complex network model

Real-world complex networks such the Internet, social networks and biological networks have increasingly attracted the interest of researchers from many areas. Accurate modelling of the statistical regularities of these large-scale networks is critical to understand their global evolving structures and local dynamical patterns. Two main families of models have been widely studied: those based on the Erdos and Renyi random graph model and those on the Barabasi-Albert scale-free model. In this paper we develop a new model: the Hybrid model, which incorporates two stages of growth. The aim of this model is to simulate the transition process between a static randomly connected network and a growing scale-free network through a tuning parameter. We measure the Hybrid model by extensive numerical simulations, focusing on the critical transition point from Poisson to Power-law degree distribution.