Let C and D be two distinct coteries under the vertex set V of a graph G = (V, E) that models a distributed system. Coterie C is said to G-dominate D (with respect to G) if the following condition holds: For any connected subgraph H of G thatcontains a quorum in D (as a subset of its vertex set), there exists a connected subgraph H′ of H that contains a quorum in C. Acoterie C on a graph G is said to be G-nondominated (G-ND) (with respect to G) if no coterie D (≠ C) on G G-dominates C.Intuitively, a G-ND coterie consists of irreducible quorums. This paper characterizes G-ND coteries in graph theoretical terms, and presents a procedure for deciding whether or not a givencoterie C is G-ND with respect to a given graph G, based on this characterization. We then improve the time complexity of thedecision procedure, provided that the given coterie C is nondominated in the sense of Garcia-Molina and Barbara. Finally, wecharacterize the class of graphs G on which the majority coterie is G-ND.