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Spatial data is fundamental in many applications like map services, land resource management, etc. Meanwhile, spatial data inherently comes with abundant context information because spatial entities themselves possess different properties, e.g., graph or textual information, etc. Among all these compound spatial data, geospatial graph data is one of the most challenging for the complexity of graph data. Graph data is commonly used to model real scenarios and searching for the matching subgraphs is fundamental in retrieving and analyzing graph data. With the ubiquity of spatial data, vertexes or edges in graphs are enriched with spatial location attributes side by side with other non-spatial attributes. Graph-based applications integrate spatial data into the graph model and provide more spatial-aware services. The co-existence of the graph and spatial data in the same geospatial graph triggers some new applications. To solve new problems in these applications, existing solutions develop an integrated system that incorporates the graph database and spatial database engines. However, existing approaches suffer from the architecture where graph data and spatial data are isolated. In this dissertation, I will explain two indexing frameworks, GeoReach and RisoTree, which can significantly accelerate the queries in geospatial graphs. GeoReach includes a query operator that adds spatial data awareness to a graph database management system. In GeoReach, the neighborhood spatial information is summarized and stored on each vertex in the graph. The summarization includes three different structures according to the location distribution. These spatial summaries are utilized to terminate the graph search early.RisoTree is a hierarchical tree structure where each node is represented by a minimum bounding rectangle (MBR). The MBR of a node is a rectangle that encloses all its children. A key difference between RisoTree and RTree is that RisoTree contains pre-materialized subgraph information to each index node. The subgraph information is utilized during the spatial index search phase to prune search paths that cannot satisfy the query graph pattern. The RisoTree index reduces the search space when the spatial filtering phase is performed with relatively light cost.