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Most work in graph-based recommender systems considers a {\em static} setting where all information about test nodes (i.e., users and items) is available upfront at training time. However, this static setting makes little sense for many real-world applications where data comes in continuously as a stream of new edges and nodes, and one has to update model predictions incrementally to reflect the latest state. To fully capitalize on the newly available data in the stream, recent graph-based recommendation models would need to be repeatedly retrained, which is infeasible in practice. In this paper, we study the graph-based streaming recommendation setting and propose a compositional recommendation model -- Lightweight Compositional Embedding (LCE) -- that supports incremental updates under low computational cost. Instead of learning explicit embeddings for the full set of nodes, LCE learns explicit embeddings for only a subset of nodes and represents the other nodes {\em implicitly}, through a composition function based on their interactions in the graph. This provides an effective, yet efficient, means to leverage streaming graph data when one node type (e.g., items) is more amenable to static representation. We conduct an extensive empirical study to compare LCE to a set of competitive baselines on three large-scale user-item recommendation datasets with interactions under a streaming setting. The results demonstrate the superior performance of LCE, showing that it achieves nearly skyline performance with significantly fewer parameters than alternative graph-based models.