This paper presents Graph Magic, a package of Java classes that represents graphs. It is specifically designed for undergraduate students to use early in their studies. It combines graph visualization with ease of programming. It allows students to implement graph algorithms using high level, easy to understand methods. Students create graphs for their programs interactively. Their programs manipulate the graphs while the students continue to view them. The emphasis on interactive editing combined with interruptible viewing provides a powerful tool for student exploration of graph concepts and algorithms.