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Tenuous subgraph finding aims to detect a subgraph with few social interactions and weak relationships among nodes. Despite significant efforts have been made on this task, they are mostly carried out in view of graph-structured data. These methods depend on calculating the shortest path and need to enumerate all the paths between nodes, which suffer the combinatorial explosion. Moreover, they all lack the integration of neighborhood information. To this end, we propose a novel model named Graph Neural Network with Motif-aware for tenuous subgraph finding (GNNM), a neighborhood aggregation based GNNs framework which can capture the latent relationship between nodes. Specially, we design a GNN module to project nodes into a low dimensional vector combining the higher-order correlation within nodes based on a motif-aware module. And then design greedy algorithms in vector space to obtain a tenuous subgraph whose size is greater than a specified constraint. Particularly, considering existing evaluation indicators cannot capture the latent friendship between nodes, we introduce a novel Potential Friend(PF) concept to measure the tenuity of a graph from a new perspective. Experimental results on the real-world and synthetic datasets demonstrate that our proposed method GNNM outperforms existing algorithms in efficiency and subgraph quality.