Research question answering requires accurate retrieval and contextual understanding of scientific literature. However, current Retrieval-Augmented Generation (RAG) methods often struggle to balance complex document relationships with precise information retrieval. In this paper, we introduce Contextualized Graph Retrieval-Augmented Generation (CG-RAG), a novel framework that integrates sparse and dense retrieval signals within graph structures to enhance retrieval efficiency and subsequently improve generation quality for research question answering. First, we propose a contextual graph representation for citation graphs, effectively capturing both explicit and implicit connections within and across documents. Next, we introduce Lexical-Semantic Graph Retrieval (LeSeGR), which seamlessly integrates sparse and dense retrieval signals with graph encoding. It bridges the gap between lexical precision and semantic understanding in citation graph retrieval, demonstrating generalizability to existing graph retrieval and hybrid retrieval methods. Finally, we present a context-aware generation strategy that utilizes the retrieved graph-structured information to generate precise and contextually enriched responses using large language models (LLMs). Extensive experiments on research question answering benchmarks across multiple domains demonstrate that our CG-RAG framework significantly outperforms RAG methods combined with various state-of-the-art retrieval approaches, delivering superior retrieval accuracy and generation quality.

Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such as neuron morphology and river geomorphology, but traditional graph representation methods often overlook these specific characteristics of tree structures. To address this, we introduce a new representation learning framework tailored for geometric trees. It first features a unique message passing neural network, which is both provably geometrical structure-recoverable and rotation-translation invariant. To address the data label scarcity issue, our approach also includes two innovative training targets that reflect the hierarchical ordering and geometric structure of these geometric trees. This enables fully self-supervised learning without explicit labels. We validate our method's effectiveness on eight real-world datasets, demonstrating its capability to represent geometric trees.

Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore, merely combining individual spatial and network representations cannot reveal the underlying interaction mechanism of spatial networks. Besides, existing spatial network representation learning methods can only consider networks embedded in Euclidean space, and can not well exploit the rich geometric information carried by irregular and non-uniform non-Euclidean space. In order to address this issue, in this paper we propose a novel generic framework to learn the representation of spatial networks that are embedded in non-Euclidean manifold space. Specifically, a novel message-passing-based neural network is proposed to combine graph topology and spatial geometry, where spatial geometry is extracted as messages on the edges. We theoretically guarantee that the learned representations are provably invariant to important symmetries such as rotation or translation, and simultaneously maintain sufficient ability in distinguishing different geometric structures. The strength of our proposed method is demonstrated through extensive experiments on both synthetic and real-world datasets.