Today using complex networks for describing natural phenomena is rapidly increasing. One of the tools for studying such networks is modeling them. A variety of different models have been introduced for describing complex systems such as Random networks, Scale-Free networks and Small World networks. Each model possesses its special characteristics among them are the length of shortest path, clustering coefficient, betweenness, communities. One of the important characteristic in networks is the correlation between their vertices' degree. This property determines whether the degree of any of vertex depends on other vertices or not. The difference in structure of different models and their characteristics stems from how each of these networks forms. By changing some of formation parameters, one can create networks with particular structure and characteristics. In this thesis the effect of each Scale-Free and Small World network parameters that play a role in forming these networks or in correlation between these networks will be studied. For this purpose we use the Barab?si–Albert model for producing Scale-Free networks and Watts–Strogatz model for describing Small World networks. Also we use Pearson coefficient for calculating network correlation. We will show that as the size of the network parameters in Scale-Free network and Small World networks and the number of links attached to the new node in Scale-Free networks and the number of nearest neighbors in Small World networks increases, the correlation and the interval of its changes decreases. At the end, effective structural factors in correlation changes will be studies. We will show that the increase of correlation stems from increase in the number of intermodular connectivity and the decrease of the number of relatively branched and vice versa.