There are numerous applications that need to deal with a large graph and need to query reachability between nodes in the graph. A 2-hop cover can compactly represent the whole edge transitive closure of a graph in O(|V | · |E| 1/2 ) space, and be used to answer reachability query efficiently. However, it is challenging to compute a 2-hop cover. The existing approaches suffer from either large resource consumption or low compression rate. In this paper, we propose a hierarchical partitioning approach to partition a large graph G into two subgraphs repeatedly in a top-down fashion. The unique feature of our approach is that we compute 2-hop cover while partitioning. In brief, in every iteration of top-down partitioning, we provide techniques to compute the 2-hop cover for connections between the two subgraphs first. A cover is computed to cut the graph into two subgraphs, which results in an overall cover with high compression for the entire graph G. Two approaches are proposed, namely a node-oriented approach and an edge-oriented approach. Our approach can efficiently compute 2-hop cover for a large graph with high compression rate. Our extensive experiment study shows that the 2-hop cover for a graph with 1,700,000 nodes and 169 billion connections can be obtained in less than 30 minutes with a compression rate about 40,000 using a PC.

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Due to rapid growth of the Internet technology and new scientific/technological advances, the number of applications that model data as graphs increases, because graphs have high expressive power to model complicated structures. The dominance of graphs in real-world applications asks for new graph data management so that users can access graph data effectively and efficiently. In this paper, we study a graph pattern matching problem over a large data graph. The problem is to find all patterns in a large data graph that match a user-given graph pattern. We propose a new two-step R-join (reachability join) algorithm with filter step and fetch step based on a clusterbased join-index with graph codes. We consider the filter step as an R-semijoin, and propose a new optimization approach by interleaving R-joins with R-semijoins. We conducted extensive performance studies, and confirm the efficiency of our proposed new approaches.

Synergistic coordination between isonicotinate (ina) and 1,2‐benzenedicarboxylate (bdc) ligands under hydrothermal conditions results in the formation of two new coordination polymers, [Er7(μ3‐O)(μ3‐OH)6(bdc)3](ina)9[Cu3X4] (X=Cl, Br). Wheel‐shaped [Er36(μ3‐OH)30(μ3‐O)6(bdc)6]54+ ions form a 2D network (see picture), which is further pillared by [Cu3X4(ina)6]4− to give a 3D framework.