The clustering coefficient is one of the most important quantities characterizing complex networks. It is often said that many networks in the real world have high clustering coefficients. However, properties of the clustering coefficient itself have not been discussed much in the literature. In this paper, some fundamental properties of the clustering coefficient are studied. First we try to find the maximum value of the clustering coefficient of graphs with the given number of vertices and edges. Next we present some classes of graphs such that each member maximizes the clustering coefficient among its neighbors having the same number of vertices and edges.