Two methods for studying the consistency problems of a class of binary relation inference networks are described. One method is derived using the mathematical concepts of energy function (E(t)) and delta energy function (Delta E(t)), where both functions have closely related geometrical interpretations. By properly formulating Delta E(t) as matrix quadratic form, network convergence is shown to be directly related to the matrix property of negative semidefiniteness. The other method, which can be applied in either a discrete-time or continuous-time framework, is based on studying the eigenvalue problem for an associated state-space model of the inference network. The merits and limitations of the proposed methods are discussed, with reference to several specific examples.