Frequent coherent subgraphs can provide valuable knowledge about the underlying internal structure of a graph database, and mining frequently occurring coherent subgraphs from large dense graph databases has been witnessed several applications and received considerable attention in the graph mining community recently. In this paper, we study how to efficiently mine the complete set of coherent closed quasi-cliques from large dense graph databases, which is an especially challenging task due to the downward-closure property no longer holds. By fully exploring some properties of quasicliques, we propose several novel optimization techniques, which can prune the unpromising and redundant sub-search spaces effectively. Meanwhile, we devise an efficient closure checking scheme to facilitate the discovery of only closed quasi-cliques. We also develop a coherent closed quasi-clique mining algorithm, Cocain 1 . Thorough performance study shows that Cocain is very efficient and scalable for large dense graph databases.

Due to the ability of graphs to represent more generic and more complicated relationships among different objects, graph mining has played a significant role in data mining, attracting increasing attention in the data mining community. In addition, frequent coherent subgraphs can provide valuable knowledge about the underlying internal structure of a graph database, and mining frequently occurring coherent subgraphs from large dense graph databases has witnessed several applications and received considerable attention in the graph mining community recently. In this article, we study how to efficiently mine the complete set of coherent closed quasi-cliques from large dense graph databases, which is an especially challenging task due to the fact that the downward-closure property no longer holds. By fully exploring some properties of quasi-cliques, we propose several novel optimization techniques which can prune the unpromising and redundant subsearch spaces effectively. Meanwhile, we devise an efficient closure checking scheme to facilitate the discovery of closed quasi-cliques only. Since large databasescannot be held in main memory, we also design an A preliminary conference version of this article entitled "Coherent Closed Quasi-Clique Discovery from Large Dense Graph

Graph data have become ubiquitous and manipulating them based on similarity is essential for many applications. Graph edit distance is one of the most widely accepted measures to determine similarities between graphs and has extensive applications in the fields of pattern recognition, computer vision etc. Unfortunately, the problem of graph edit distance computation is NP-Hard in general. Accordingly, in this paper we introduce three novel methods to compute the upper and lower bounds for the edit distance between two graphs in polynomial time. Applying these methods, two algorithms AppFull and AppSub are introduced to perform different kinds of graph search on graph databases. Comprehensive experimental studies are conducted on both real and synthetic datasets to examine various aspects of the methods for bounding graph edit distance. Result shows that these methods achieve good scalability in terms of both the number of graphs and the size of graphs. The effectiveness of these algorithms also confirms the usefulness of using our bounds in filtering and searching of graphs.

To our best knowledge, all existing graph pattern mining algorithms can only mine either closed, maximal or the complete set of frequent subgraphs instead of graph generators which are preferable to the closed subgraphs according to the Minimum Description Length principle in some applications. In this paper, we study a new problem of frequent subgraph mining, called frequent connected graph generator mining, which poses significant challenges due to the underlying complexity associated with frequent subgraph mining as well as the absence of Apriori property for graph generators. Whereas, we still present an efficient solution Fogger 1 for this new problem. By exploring some properties of graph generators, two effective pruning techniques, backward edge pruning and forward edge pruning , are proposed to prune the branches of the well-known DFS code enumeration tree that do not contain graph generators. To further improve the efficiency, an effective index structure, ADI++, is also devised to facilitate the subgraph isomorphism checking. We experimentally evaluate various aspects of Fogger using both real and synthetic datasets. Our results demonstrate that the two pruning techniques are effective in pruning the unpromising parts of search space, and Fogger is efficient and scalable in terms of the base size of input databases. Meanwhile, the performance study for graph generator-based classification model shows that generator-based model is much simpler and can achieve almost the same accuracy for classifying chemical compounds in comparison with closed subgraph-based model.

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