We establish a geometrical framework for the study of imprimitive, G‐symmetric graphs Г by exploiting the fact that any G‐partition B of the vertex set VГ gives rise both to a quotient graph ГB and to a tactical configuration D(B) induced on each block B ∈ B. We also examine those cases in which D(B) is degenerate, and characterize the possible graphs Г in many cases where the quotient ГB is either a complete graph or a circuit. When D(B) is non‐degenerate, a natural extremal case occurs when D(B) is a symmetric 2‐design with stabilizer G(B) acting doubly transitively on points: we characterize such graphs in the case where ГB is complete.

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