As graph data is prevalent for an increasing number of Internet applications, continuously monitoring structural patterns in dynamic graphs in order to generate real-time alerts and trigger prompt actions becomes critical for many applications. In this paper, we present a new system GraphS to efficiently detect constrained cycles in a dynamic graph, which is changing constantly, and return the satisfying cycles in real-time. A hot point based index is built and efficiently maintained for each query so as to greatly speed-up query time and achieve high system throughput. The GraphS system is developed at Alibaba to actively monitor various online fraudulent activities based on cycle detection. For a dynamic graph with hundreds of millions of edges and vertices, the system is capable to cope with a peak rate of tens of thousands of edge updates per second and find all the cycles with predefined constraints with a 99.9% latency of 20 milliseconds.

Graph is a ubiquitous structure representing entities and their relationships applied in many areas such as social networks, web graphs, and biological networks. One of the fundamental tasks in graph analytics is to investigate the relations between two vertices (e.g., users, items and entities) such as how a vertex A influences another vertex B, or to what extent A and B are similar to each other, based on the graph topology structure. For this purpose, we study the problem of hop-constrained s-t simple path enumeration in this paper, which aims to list all simple paths from a source vertex s to a target vertex t with hop-constraint k. We first propose a polynomial delay algorithm, namely BC-DFS, based on barrier-based pruning technique. Then a join-oriented algorithm, namely JOIN, is designed to further enhance the query response time. On the theoretical side, BC-DFS is a polynomial delay algorithm with O(km) time per output where m is the number of edges in the graph. This time complexity is the same as the best known theoretical result for the polynomial delay algorithms of this problem. On the practical side, our comprehensive experiments on 15 real-life networks demonstrate the superior performance of the BC-DFS algorithm compared to the stateof-the-art techniques. It is also reported that the JOIN algorithm can further significantly enhance the query response time.

As uncertainty is inherent in a wide spectrum of graph applications such as social network and brain network, it is highly demanded to re-visit classical graph problems in the context of uncertain graphs. Driven by real-applications, in this paper, we study the problem of k-core computation on uncertain graphs and propose a new model, namely (,)-core, which consists of nodes with probability at least to be kcore member in the uncertain graph. We show the computation of (,)-core is NP-hard, and hence resort to sampling based methods. Effective and efficient pruning techniques are proposed to significantly reduce the candidate size. To further reduce the cost of k-core computation on multiple sampled graphs, we design a k-core membership check algorithm following a novel expansion-based search paradigm. Extensive experiments on reallife graphs demonstrate the effectiveness and efficiency of our proposed techniques.

In this paper, we study the problem of label-constrained reachability (LCR) query which is fundamental in many applications with directed edge-label graphs. Although the classical reachability query (i.e., reachability query without label constraint) has been extensively studied, LCR query is much more challenging because the number of possible label constraint set is exponential to the size of the labels. We observe that the existing techniques for LCR queries only construct partial index for better scalability, and their worst query time is not guaranteed and could be the same as an online breadth-first search (BFS). In this paper, we propose novel label-constrained 2-hop indexing techniques with novel pruning rules and order strategies. It is shown that our worst query time could be bounded by the in-out index entry size. With all these techniques, comprehensive experiments show that our proposed methods significantly outperform the state-of-the-art technique in terms of query response time (up to 5 orders of magnitude speedup), index size and index construction time. In particular, our proposed method can answer LCR queries within microsecond over billion-scale graphs in a single machine.

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