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In the paper a class of locally derivable graphs is defined and discussed. Well known particular cases of derivable graphs are (among others) trees, complete, and triangular graphs; in the paper a broader class of locally derivable graphs, called closed graphs, is defined. Nodes and edges of closed graphs can be partitioned into external and internal ones; the main property of such graphs their local reducibility: successive removing its external nodes leads eventually to a singleton, and removing its external edges leads to an a spanning tree of the graph. The class of closed graphs is then a class enabling structural reducing. This property can be applied in processor networks to design some local procedures leading to global results.