Graph languages defined by hyperedge replacement (HR) grammars can beNP-complete. We study predictive shift-reduce (PSR) parsing for a subclass ofthese grammars, which generalizes the concepts of SLR(1) string parsing tographs. PSR parsers run in linear space and time. In comparison to thepredictive top-down (PTD) parsers recently developed by the authors, PSRparsers are more efficient, and allow parsing for a wider class of HR grammars,while the analysis of PSR parsability is easier than for PTD parsing.