Graph representation has evolved from the simple nodes and edges model to the ones with more information embedded representations. One such representation is the knowledge graphs which are a type of digraphs in which edges are labeled with data displaying the relationship between a source and a target. Another main graph type is the uncertain graphs where an edge is labeled with a probability showing its existence. In this chapter, we describe these three main contemporary graph types and their algorithms which play important roles in artificial intelligence methods. We also review main graph mining methods which are used to discover structures in the graphs.