Blockchain technology has transformed financial services sectors by providing security, transparency, and immutability through decentralized ledger systems. However, while blockchain data can support a range of applications-such as user quality analysis, illegal activity detection, and transaction pattern identification-existing systems are restricted to basic queries on blocks and transactions due to their sequential data storage. To support queries more generally, we propose VGQ, the first verifiable graph query (VGQ) framework that enables efficient graph queries on blockchain systems without altering blockchain storage structures. VGQ integrates a query layer with an external graph database system and represents blockchain data as a directed transaction graph to improve the efficiency of graph query execution. To ensure reliable results, VGQ includes result verification with three key performance enhancing optimizations: (i) computing connected components to exclude irrelevant vertices and edges during verification; (ii) merging information from edges to accelerate completeness verification; and (iii) employing a dual pointer algorithm for efficient soundness verification. Experiments offer evidence that VGQ can improve on the state-of-the-art framework in terms of query efficiency by up to one order of magnitude and in terms of verification efficiency by up to two orders of magnitude.

Community search on bipartite graphs has been extensively studied in suspicious-group detection and team formation. However, the existing studies focused on the cohesiveness of the community, but ignored the size constraint on bipartite graphs , potentially leading to large community sizes and high costs. In this study, a size-constrained ( α , β )–community (SCC) containing a query vertex on a bipartite graph was investigated, where the upper layer size of the community cannot exceed threshold s and the lower layer size cannot exceed threshold t . For supporting SCC search in different situations, two search methods—peeling and expansion—are proposed by peeling from the ( α , β )-core containing the query vertex and expanding from the query vertex respectively. An efficient lower bound based on degree gap is proposed by terminating unpromising search branches early to increase the efficiency of the community search. The experimental results indicated that the proposed methods can be used to find communities within the size thresholds, with the efficiency of the search increased based on the lower bound.

SimRank is a significant metric to measure the similarity of nodes in graph data analysis. The problem of SimRank computation has been studied extensively, however there is no existing work that can provide one unified algorithm to support the SimRank computation both on static and temporal graphs. In this work, we first propose CrashSim, an index-free algorithm for single-source SimRank computation in static graphs. CrashSim can provide provable approximation guarantees for the computational results in an efficient way. In addition, as the reallife graphs are often represented as temporal graphs, CrashSim enables efficient computation of SimRank in temporal graphs. We formally define two typical SimRank queries in temporal graphs, and then solve them by developing an efficient algorithm based on CrashSim, called CrashSim-T. From the extensive experimental evaluation using five real-life and synthetic datasets, it can be seen that the CrashSim algorithm and CrashSim-T algorithm substantially improve the efficiency of the state-of-the-art SimRank algorithms by about 30%, while achieving the precision of the result set with about 97%.