In this paper, we explore a novel solution of constructing a heterogeneous graph for each instance by leveraging aspect-focused and inter-aspect contextual dependencies for the specific aspect and propose an Interactive Graph Convolutional Networks (InterGCN) model for aspect sentiment analysis. Specifically, an ordinary dependency graph is first constructed for each sentence over the dependency tree. Then we refine the graph by considering the syntactical dependencies between contextual words and aspect-specific words to derive the aspect-focused graph. Subsequently, the aspect-focused graph and the corresponding embedding matrix are fed into the aspect-focused GCN to capture the key aspect and contextual words. Besides, to interactively extract the inter-aspect relations for the specific aspect, an inter-aspect GCN is adopted to model the representations learned by aspect-focused GCN based on the inter-aspect graph which is constructed by the relative dependencies between the aspect words and other aspects. Hence, the model can be aware of the significant contextual and aspect words when interactively learning the sentiment features for a specific aspect. Experimental results on four benchmark datasets illustrate that our proposed model outperforms state-of-the-art methods and substantially boosts the performance in comparison with BERT.