There exists a wide variety of complex networks, ranging from biology to sociology. Various real world networks can be depicted as complex networks. These networks have different structures and communication patterns. In this paper we have discussed their structures and corresponding examples that demonstrates the behavior of the networks. The structure is helpful to recognize the communication in a network. Earlier, there were small networks with few vertices and edges. But nowadays large complex networks have come into existence. Many researchers are trying to unfold the characteristics which will help to understand the complex networks in a better way. In this paper we have discussed various properties and their effects on different networks. These properties define the non-random nature of complex networks. They have significant impact on the network's structure. We have tried to describe complex network structures from various researchers' point of view.