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Centrality is a family of metrics for characterizing the importance of a vertex in a graph. Although a large number of centrality metrics have been proposed, a majority of them ignores uncertainty in graph data. In this article, we formulate closeness centrality on uncertain graphs and define the batch closeness centrality evaluation problem that computes the closeness centrality of a subset of vertices in an uncertain graph. We develop three algorithms, MS-BCC, MG-BCC, and MGMS-BCC, based on sampling to approximate the closeness centrality of the specified vertices. All these algorithms require to perform breadth-first searches (BFS) starting from the specified vertices on a large number of sampled possible worlds of the uncertain graph. To improve the efficiency of the algorithms, we exploit operation-level parallelism of the BFS traversals and simultaneously execute the shared sequences of operations in the breadth-first searches. Parallelization is realized at different levels in these algorithms. The experimental results show that the proposed algorithms can efficiently and accurately approximate the closeness centrality of the given vertices. MGMS-BCC is faster than both MS-BCC and MG-BCC because it avoids more repeated executions of the shared operation sequences in the BFS traversals. [ABSTRACT FROM AUTHOR]

In many real applications, graph data is subject to uncertainties due to incompleteness and imprecision of data. Mining such uncertain graph data is semantically different from and computationally more challenging than mining conventional exact graph data. This paper investigates the problem of mining uncertain graph data and especially focuses on mining frequent subgraph patterns on an uncertain graph database. A novel model of uncertain graphs is presented, and the frequent subgraph pattern mining problem is formalized by introducing a new measure, called expected support. This problem is proved to be NP-hard. An approximate mining algorithm is proposed to find a set of approximately frequent subgraph patterns by allowing an error tolerance on expected supports of discovered subgraph patterns. The algorithm uses efficient methods to determine whether a subgraph pattern can be output or not and a new pruning method to reduce the complexity of examining subgraph patterns. Analytical and experimental results show that the algorithm is very efficient, accurate, and scalable for large uncertain graph databases. To the best of our knowledge, this paper is the first one to investigate the problem of mining frequent subgraph patterns from uncertain graph data. [ABSTRACT FROM AUTHOR]