Title: Graph in Graph Neural Network. Abstract: Most existing Graph Neural Networks (GNNs) frequently suffer from two limitations: (i) they can only process graphs whose vertices are represented by vectors or single values; and (ii) they assume each input graph is independent from others during the propagation. In this paper, we propose \textbf{the first GNN model (called Graph in Graph Neural Network (GIG)) that can process graphs whose vertices are also represented by graphs}. Considering that the relationship between different graphs may contain crucial task-related cues, we further propose a GIG graph relationship modelling (GRM) strategy that integrates multiple target graph samples as a global graph, each of whose vertex describes a target graph sample. We then applies the GIG model to jointly process the combined graph samples (i.e., the global graph), where additional task-specific relationship cues among graph samples can be extracted in an end-to-end manner. The experimental results show that the proposed GIG model and the GRM strategy generalize well on various graph analysis tasks, providing new state-of-the-art results on five out of seven benchmark graph datasets. Importantly, not only its vertex/edge updating functions are flexible to be customized from different existing GNNs but also it is robust to different settings. Our code is provided in the supplementary material for reproducibly purpose.