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This paper is proposing an integration-based approach to trace a specific eigenvalue or a set of eigenvalues of a power system network. Indices are developed to identify critical eigenvalue to be traced for further analysis. This index takes into account the rate of change as well as the direction of movement. The rate of change is with respect to any parameter variation of interest. It finally provides information related to oscillatory stability and margin requirements to maintain a specific damping ratio. Eigenvalue and eigenvector sensitivities (with respect to any explicit/implicit parameters) are by-products of this approach.