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Random graphs are extensive, in addition, it is used in several functional areas of research, particularly in the field of complex networks. The study of complex networks is a useful and active research areas in science, such as electrical power grids and telecommunication networks, collaboration and citation networks of scientists,protein interaction networks, World-Wide Web and Internet Social networks, etc. A social network is a graph in which n vertices and m edges are selected at random, the vertices represent people and the edges represent relationships between them. In network analysis, the number of properties is defined and studied in the literature to identify the important vertex in a network. Recent studies have focused on statistical and structural properties such as diameter, small world effect, clustering coefficient, centrality measure, modularity, community structure in social networks like Facebook, YouTube, Twitter, etc. In this paper, we first provide a brief introduction to the complex network properties. We then discuss the complex network properties with values expected for random graphs.

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