Recent interest in complex networks has catalyzed the development of numerous models to help artificially generate and understand these networks. Watts and Strogatz presented a model (Watts Strogatz 1998) to explain how the two properties of small world networks, high clustering coefficient and low average path length appear in networks. (Barabasi and Albert 1999) gave a model to explain how networks with power-law degree distribution arise in networks. From these two ground breaking results, many researchers have introduced different models to explain the appearance of networks with small world and scale free properties in the real world. In this paper, we focus on social networks and comparatively study the structure of real world and artificially generated networks. The differences and similarities of different models are highlighted and their shortcomings are identified. Further more, we present a new model which produces networks with both small world and scale free properties which are structurally more similar to real world social networks.