As you propably know, a process (in terms of process algebra like CSP) can consume an input and will the behave like another process (unless it is a process that does not accept input, usually called STOP).
You can construct a graph where the nodes are the processes and the outgoing edges the input that the node can consume, directed to the node (process) that gives the new behaivior. If such a graph contains a directed path back to a starting node (i.e., a circle), you have an infinite process.
Finding a circle in a graph is a standard problem in graph theory and is usually done by DFS.
A good introduction to CSP is Tony Hoare's Book on that subject, what is easy to read also for beginners. (However, Hoare does not use the term "process graph" but talks only on "graphs".) The standard text book for CCS is Milner's "Communication and Concurrency" published by Prentice Hall.