This paper extends the notion of slicing, which was originally proposed and studied for sequential programs, to concurrent programs and presents a graph-theoretical approach to slicing concurrent programs. In addition to the usual control and data dependences proposed and studied for sequential programs, the paper introduces three new types of primary program dependences in concurrent programs, named the selection dependence, synchronization dependence, and communication dependence. The paper also propose a new program representation for concurrent programs, named the Process Dependence Net (PDN), which is an arc-classified digraph to explicitly represent the five types of primary program dependences in the programs. As a result, various notions about slicing concurrent programs can be formally defined based on the representation, and the problem of slicing a concurrent program can be simply reduced to a vertex reachability problem in its PDN representation.