This paper proposes a method for storing graphs and defining graph algorithms based on the well-developed relational database. In this method, graphs are represented in the form of relations. Each vertex and edge of a graph is represented as tuples of the table and saved in a database. We developed a library of graph operations for the storage and management of graphs and the development of graph applications. Furthermore, we defined graph algorithms in terms of relational algebraic operations such as projection, selection, and join. They can be implemented with the database language such as SQL. This database approach provides an efficient methodology to deal with very large-scale graphs and to support the development of graph applications.