We propose the Edge-Grouped Reduced-Rank Network Autoregressive model (Edge-Grouped RRNAR) for multivariate time series observed over a network. The model allows transmission effects to vary across prespecified and economically interpretable groups of edges, while using a low-rank structure to capture cross-variable dynamics. This structure separates where network transmission occurs from which variables transmit and respond. We develop a topology-aware and block-specific scaled gradient descent algorithm with a convex low-rank initialization, and establish its local linear convergence and non-asymptotic estimation rates. We further derive asymptotic normality for the estimated transition matrix and normalized grouped network coefficients, enabling Wald tests for network relevance and edge-group homogeneity. Simulations demonstrate the finite-sample performance of the proposed estimation and inference procedures. An application to quarterly U.S. industry data linked by the production network reveals distinct predictive transmission intensities across economically defined edge groups, identifies interpretable real-activity and price-cost channels, and improves forecasting relative to standard network and matrix autoregressive models.

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