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Networked time series are time series on a graph, one for each node, with applications in traffic and weather monitoring. Graph neural networks are natural candidates for networked time series imputation and have recently outperformed existing alternatives such as recurrent and generative models for time series imputation as they utilize a relational inductive bias for imputation. However, existing GNN-based approaches fail to capture the higher-order topological structure between sensors, which are shaped by recurring substructures in the graph, referred to as temporal motifs. In addition, it remains uncertain which motifs are the most pivotal motifs guiding the imputation task in networked time series. In this paper, we fill in this gap by proposing a graph neural network designed to leverage motif structures within the network by employing weighted motif adjacency matrices to capture higher-order neighborhood information. In particular, (1) we design a motif-wise multi-view attention module that explicitly captures various higher-order structures along with an attention mechanism that automatically assigns high weights to informative ones in order to maximize the use of higher-order information. (2) We introduce a gated fusion module by merging gated recurrent networks and graph convolutional networks to capture the spatial and temporal dependency in order to reflect the intricate impacts of temporal and spatial influence. Experimental results demonstrate that when compared to state-of-the-art models for time-series imputation tasks, our proposed model can reduce the error by around 19%.