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Graph pattern matching (GPM) can be used to mine the key information in graphs. Exact GPM is one of the most commonly used methods among all the GPMrelated methods, which aims to exactly find all subgraphs for a given query graph in a data graph. The exact GPM has been widely used in biological data analyses, social network analyses and other fields. In this paper, the applications of the exact GPM were first introduced, and the research progress of the exact GPM was summarized. Then, the related algorithms were introduced in detail, and the experiments on the state-of-the-art exact GPM algorithms were conducted to compare their performance. Based on the experimental results, the applicable scenarios of the algorithms were pointed out. New research opportunities in this area were proposed. [ABSTRACT FROM AUTHOR]

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The subgraph matching problem associated with large graphs is an emerging research challenge in graph search due to the growing size of the web, social, and metabolic graphs, and the wide availability of graph databases. Such problems involve finding all instances (aka embedding) of the small-sized query graph in the associated large-sized reference graph. Many state-of-the-art algorithms, including VF3, RI, CFL-Match, and Glasgow, exist to solve subgraph matching problem. RI is one of the fastest subgraph matching algorithms focusing mainly on time efficiency performance measures. However, other performance measures, such as the number of found instances of the query graph (embedding count), the method of ordering the query graph's vertices, and the number of recursive calls, are crucial for the efficiency and effectiveness of the subgraph matching. In this paper, the RI+ algorithm is proposed as an enhanced version of RI, which has been designed using candidate region-based decomposition and ordering. Three novel candidate region orderings have been introduced, namely vertex-count, density, and average-path-length, based on the structural properties of the candidate regions. On empirical analysis of RI+ on real-world data sets, it was observed that RI+ shows significant improvement in efficiency and effectiveness over RI on both performance evaluation measures, namely, embedding count and search time. The influence of the proposed candidate region orderings on the search time of RI+ was also analyzed, revealing that a suitable candidate region ordering has the potential to improve the search time of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Frequent subgraph mining (FSM) is defined as finding all the subgraphs in a given graph that appear more number of times than a given value. It consists of two steps broadly, first is generating a candidate subgraph and second is calculating support of that subgraph. When the input to FSM algorithm is a single graph, calculating support of subgraph needs identifying its isomorphisms in the input graph. Identifying subgraph isomorphisms is NP-Complete problem. Evidently, fewer the number of candidates, fewer the support computations needed. In this paper we present a filtration technique that reduces the number of candidate subgraphs thereby reducing the overall time complexity by 7 to 18% experimentally. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) model reconstruction needs to resolve the association problem of precursory 3D process model and process drawing. An approach based on the attribute adjacency graph of the primitive combination units is proposed. By extracting the primitive combination units of process drawing and the projection drawings of the precursory 3D process model, the process drawing and the projection drawings was presented in an attribute adjacency graph. According to the attributes of the vertexes and edges, whether the two attribute adjacency graphs were isomorphism were judged, and the association problem of precursory 3D process model and process drawing was translated to the matching problem of attribute adjacency graphs. Taking the side plate part as an example, the experimental result shows that this method realizes the association of precursory 3D process model and process drawing. [ABSTRACT FROM AUTHOR]

In recent years, interest has been growing in the study of complex networks. Since Erdös and Rényi (1960) proposed their random graph model about 50 years ago, many researchers have investigated and shaped this field. Many indicators have been proposed to assess the global features of networks. Recently, an active research area has developed in studying local features named motifs as the building blocks of networks. Unfortunately, network motif discovery is a computationally hard problem and finding rather large motifs (larger than 8 nodes) by means of current algorithms is impractical as it demands too much computational effort. In this paper, we present a new algorithm (MODA) that incorporates techniques such as a pattern growth approach for extracting larger motifs efficiently. We have tested our algorithm and found it able to identify larger motifs with more than 8 nodes more efficiently than most of the current state-of-the-art motif discovery algorithms. While most of the algorithms rely on induced subgraphs as motifs of the networks, MODA is able to extract both induced and non-induced subgraphs simultaneously. The MODA source code is freely available at: http://LBB.ut.ac.ir/Download/LBBsoft/MODA/ [ABSTRACT FROM AUTHOR]

Abstract: We introduce classes of graphs with bounded expansion as a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r, . We generalize to these classes some results proved for proper minor closed classes and bounded degree graphs, such as the existence of low tree-width colorings, a linear time algorithm to check subgraph isomorphism for a fixed pattern and homomorphism dualities. [Copyright &y& Elsevier]