The k-truss is a type of cohesive subgraphs proposed recently for the study of networks. While the problem of computing most cohesive subgraphs is NP-hard, there exists a polynomial time algorithm for computing k-truss. Compared with k-core which is also efficient to compute, k-truss represents the "core" of a k-core that keeps the key information of, while filtering out less important information from, the k-core. However, existing algorithms for computing k-truss are inefficient for handling today's massive networks. We first improve the existing in-memory algorithm for computing k-truss in networks of moderate size. Then, we propose two I/O-efficient algorithms to handle massive networks that cannot fit in main memory. Our experiments on real datasets verify the efficiency of our algorithms and the value of k-truss.

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We study the problem of processing subgraph queries on a database that consists of a set of graphs. The answer to a subgraph query is the set of graphs in the database that are supergraphs of the query. In this article, we propose an efficient index, FG*-index, to solve this problem.The cost of processing a subgraph query using most existing indexes mainly consists of two parts, the index probing cost and the candidate verification cost. Index probing is to find the query in the index, or to find the graphs from which we can generate a candidate answer set for the query. Candidate verification is to test whether each graph in the candidate set is indeed a supergraph of the query. We design FG*-index to minimize these two costs as follows.FG*-index consists of three components: the FG-index, the feature-index, and the FAQ-index. First, the FG-index employs the concept of Frequent subGraph (FG) to allow the set of queries that are FGs to be answered without candidate verification. We call this set of queries FG-queries. We can enlarge the set of FG-queries so that more queries can be answered without candidate verification; however, a larger set of FG-queries implies a larger FG-index and hence the index probing cost also increases. We propose the feature-index to reduce the index probing cost. The feature-index uses features to filter false results that are matched in the FG-index, so that we can quickly find the truly matching graphs for a query. For processing non-FG-queries, we propose the FAQ-index, which is dynamically constructed from the set of Frequently Asked non-FG-Queries (FAQs). Using the FAQ-index, verification is not required for processing FAQs and only a small number of candidates needs to be verified for processing non-FG-queries that are not frequently asked. Finally, a comprehensive set of experiments verifies that query processing using FG*-index is up to orders of magnitude more efficient than state-of-the-art indexes and it is also more scalable.

Shortest path is a fundamental graph problem with numerous applications. However, the concept of classic shortest path is insufficient or even flawed in a temporal graph, as the temporal information determines the order of activities along any path. In this paper, we show the shortcomings of classic shortest path in a temporal graph, and study various concepts of "shortest" path for temporal graphs. Computing these temporal paths is challenging as subpaths of a "shortest" path may not be "shortest" in a temporal graph. We investigate properties of the temporal paths and propose efficient algorithms to compute them. We tested our algorithms on real world temporal graphs to verify their efficiency, and also show that temporal paths are essential for studying temporal graphs by comparing shortest paths in normal static graphs.

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