This work demonstrates for the first time the application of network topology of variance decompositions in analyzing the connectedness of chemical plant process variable oscillations arising from disturbances and faults. Specifically, the time-based connectedness and frequency-based connectedness of variables can be used to compute the net pairwise dynamic connectedness (NPDC), which originated as a volatility spillover index for financial markets studies in the field of econometrics. This work used the anomaly-detection benchmark Tennessee-Eastman chemical process (TEP) dataset, which consists of 41 measured variables and 11 manipulated variables subjected to various faulty operating conditions. The data analytics was performed using key functions from the R-package ‘ConnectednessApproach’ that implements connectedness computations based on time and frequency. The NPDC coefficient matrices were then transformed into network adjacency matrices for the rendering of the network topology of connectedness for TEP. The resulting network topologies allow a comprehensive analysis of oscillation effects across all plant-measured and manipulated variables. Analyzing the directed connectedness of the system dynamics at short-range, mid-range, and long-range frequencies showed how the oscillation effects of disturbances and faults propagate and dissipate in the short-term, mid-term, and long-term periods.