The goal of community search is to obtain compact subgraphs containing query vertices from data graphs， and community search is widely used in sociology， biology， and other fields. In view of the fact that the basic connectivity structures of the existing community models based on subgraph connectivity are all completely connected graphs， which cannot meet the needs of users for the diversity of community structures in practical applications， a community search method based on motif connectivity was proposed， including Motif-Connective Community （MCC） model based on motif connectivity and two corresponding community search algorithms — MPCS （Motif-Processed Community Search） algorithm and MP-index based community search algorithm. MCC model was able to help users freely specify the basic connectivity structure of community， and MPCS algorithm was able to be used to solve the search problem of MCC. Furthermore， two pruning optimization techniques were proposed for the motif instance search process and the belonged community judgment process. Finally， the MP-index forest was designed to avoid redundant traversal operations in the process of community search. Experimental results on multiple real datasets show that the pruning optimization can reduce the running time of MPCS algorithm by 60% to 85%， and the efficiency of the community search algorithm based on MP-index forest is improved by two to three orders of magnitude compared with the efficiency of MPCS algorithm added with pruning optimization. It can be seen that the proposed method has practical application values in commodity recommendation， social network and other issues.

The k-step reachability query is used to answer whether there exists a path between two nodes with length no longer than k in a Directed Acyclic Graph （DAG）. Concerning the problems of large index size and low query processing efficiency of existing approaches， a bi-directional shortest path index based on partial nodes was proposed to improve the coverage of reachable queries， and a set of optimization rules was proposed to reduce the index size. Then， a bi-directional reversed topological index was proposed to accelerate the unreachable queries answering based on the simplified graph. Finally， the farthest-node-first-visiting bi-traversal strategy was proposed to improve the efficiency of query processing. Experimental results on 21 real datasets， such as citation networks and social networks， show that compared with existing efficient approaches including PLL （Pruned Landmark Labeling） and BFSI-B （Breadth First Search Index-Bilateral）， the proposed algorithm has smaller index size and higher query response speed.