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Efficient Aggregation for Graph Summarization
"... Graphs are widely used to model real world objects and their relationships, and large graph datasets are common in many application domains. To understand the underlying characteristics of large graphs, graph summarization techniques are critical. However, existing graph summarization methods are mo ..."
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Cited by 81 (5 self)
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Graphs are widely used to model real world objects and their relationships, and large graph datasets are common in many application domains. To understand the underlying characteristics of large graphs, graph summarization techniques are critical. However, existing graph summarization methods are mostly statistical (studying statistics such as degree distributions, hopplots and clustering coefficients). These statistical methods are very useful, but the resolutions of the summaries are hard to control. In this paper, we introduce two databasestyle operations to summarize graphs. Like the OLAPstyle aggregation methods that allow users to drilldown or rollup to control the resolution of summarization, our methods provide an analogous functionality for large graph datasets. The first operation, called SNAP, produces a summary graph by grouping nodes based on userselected node attributes and relationships. The second operation, called kSNAP, further allows users to control the resolutions of summaries and provides the “drilldown ” and “rollup ” abilities to navigate through summaries with different resolutions. We propose an efficient algorithm to evaluate the SNAP operation. In addition, we prove that the kSNAP computation is NPcomplete. We propose two heuristic methods to approximate the kSNAP results. Through extensive experiments on a variety of real and synthetic datasets, we demonstrate the effectiveness and efficiency of the proposed methods.
Fgindex: towards verificationfree query processing on graph databases
 in SIGMOD, 2007
"... Graphs are prevalently used to model the relationships between objects in various domains. With the increasing usage of graph databases, it has become more and more demanding to efficiently process graph queries. Querying graph databases is costly since it involves subgraph isomorphism testing, whic ..."
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Cited by 75 (9 self)
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Graphs are prevalently used to model the relationships between objects in various domains. With the increasing usage of graph databases, it has become more and more demanding to efficiently process graph queries. Querying graph databases is costly since it involves subgraph isomorphism testing, which is an NPcomplete problem. In recent years, some effective graph indexes have been proposed to first obtain a candidate answer set by filtering part of the false results and then perform verification on each candidate by checking subgraph isomorphism. Query performance is improved since the number of subgraph isomorphism tests is reduced. However, candidate verification is still inevitable, which can be expensive when the size of the candidate answer set is large. In this paper, we propose a novel indexing technique that constructs a nested invertedindex, called FGindex, based on the set of Frequent subGraphs (FGs). Given a graph query that is an FG in the database, FGindex returns the exact set of query answers without performing candidate verification. When the query is an infrequent graph, FGindex produces a candidate answer set which is close to the exact answer set. Since an infrequent graph means the graph occurs in only a small number of graphs in the database, the number of subgraph isomorphism tests is small. To ensure that the index fits into the main memory, we propose a new notion of δTolerance Closed Frequent Graphs (δTCFGs), which allows us to flexibly tune the size of the index in a parameterized way. Our extensive experiments verify that query processing using FGindex is orders of magnitude more efficient than using the stateoftheart graph index.
Graph database indexing using structured graph decomposition
 In ICDE
, 2007
"... We introduce a novel method of indexing graph databases in order to facilitate subgraph isomorphism and similarity queries. The index is comprised of two major data structures. The primary structure is a directed acyclic graph which contains a node for each of the unique, induced subgraphs of the da ..."
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Cited by 56 (5 self)
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We introduce a novel method of indexing graph databases in order to facilitate subgraph isomorphism and similarity queries. The index is comprised of two major data structures. The primary structure is a directed acyclic graph which contains a node for each of the unique, induced subgraphs of the database graphs. The secondary structure is a hash table which crossindexes each subgraph for fast isomorphic lookup. In order to create a hash key independent of isomorphism, we utilize a codebased canonical representation of adjacency matrices, which we have further refined to improve computation speed. We validate the concept by demonstrating its effectiveness in answering queries for two practical datasets. Our experiments show that for subgraph isomorphism queries, our method outperforms existing methods by more than an order of magnitude. 1.
Treepi: A novel graph indexing method
 in Proc. of ICDE
, 2007
"... Graphs are widely used to model complex structured data such as XML documents, protein networks, and chemical compounds. One of the fundamental problems in graph databases is efficient search and retrieval of graphs using indexing techniques. In this paper, we study the problem of indexing graph da ..."
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Cited by 52 (2 self)
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Graphs are widely used to model complex structured data such as XML documents, protein networks, and chemical compounds. One of the fundamental problems in graph databases is efficient search and retrieval of graphs using indexing techniques. In this paper, we study the problem of indexing graph databases using frequent subtrees as indexing structures. Trees can be manipulated efficiently while preserving a lot of structural information of the original graphs. In our proposed method, frequent subtrees of a database are selected as the feature set. To save memory, the set of feature trees is shrunk based on a support threshold function and their discriminative power. A treepartition based query processing scheme is proposed to perform graph queries. The concept of Center Distance Constraints is introduced to prune the search space. Furthermore, a new algorithm which utilizes the location information of indexing structures is used to perform subgraph isomorphism tests. We apply our method on a wide range of real and synthetic data to demonstrate the usefulness and effectiveness of this approach. 1
Discovering informative connection subgraphs in multirelational graphs
 SIGKDD Explorations
, 2005
"... Discovering patterns in graphs has long been an area of interest. In most approaches to such pattern discovery either quantitative anomalies, frequency of substructure or maximum flow is used to measure the interestingness of a pattern. In this paper we introduce heuristics that guide a subgraph dis ..."
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Cited by 36 (7 self)
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Discovering patterns in graphs has long been an area of interest. In most approaches to such pattern discovery either quantitative anomalies, frequency of substructure or maximum flow is used to measure the interestingness of a pattern. In this paper we introduce heuristics that guide a subgraph discovery algorithm away from banal paths towards more “informative ” ones. Given an RDF graph a user might pose a question of the form: “What are the most relevant ways in which entity X is related to entity Y? ” the response to which is a subgraph connecting X to Y. We use our heuristics to discover informative subgraphs within RDF graphs. Our heuristics are based on weighting mechanisms derived from edge semantics suggested by the RDF schema. We present an analysis of the quality of the subgraphs generated with respect to path ranking metrics. We then conclude presenting intuitions about which of our weighting schemes and heuristics produce higher quality subgraphs.
Comparing Graph Representations of Protein Structure for Mining FamilySpecific ResidueBased Packing Motifs
 Journal of Computational Biology
, 2005
"... We find recurring aminoacid residue packing patterns, or spatial motifs, that are characteristic of protein structural families, by applying a novel frequent subgraph mining algorithm to graph representations of protein threedimensional structure. Graph nodes represent amino acids, and edges are c ..."
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Cited by 36 (5 self)
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We find recurring aminoacid residue packing patterns, or spatial motifs, that are characteristic of protein structural families, by applying a novel frequent subgraph mining algorithm to graph representations of protein threedimensional structure. Graph nodes represent amino acids, and edges are chosen in one of three ways: first, using a threshold for contact distance between residues; second, using Delaunay tessellation; and third, using the recently developed almostDelaunay edges. For a set of graphs representing a protein family from the Structural Classification of Proteins (SCOP) database, subgraph mining typically identifies several hundred common subgraphs corresponding to spatial motifs that are frequently found in proteins in the family but rarely found outside of it. We find that some of the large motifs map onto known functional regions in two protein families explored in this study, i.e., serine proteases and kinases. We find that graphs based on almostDelaunay edges significantly reduce the number of edges in the graph representation and hence present computational advantage, yet the patterns extracted from such graphs have a biological interpretation approximately equivalent to that of those extracted from distance based graphs. Key words: protein structure motifs, frequent subgraph mining, almostDelaunay. 1.
Discovering Frequent Topological Structures from Graph Datasets
"... The problem of finding frequent patterns from graphbased datasets is an important one that finds applications in drug discovery, protein structure analysis, XML querying, and social network analysis among others. In this paper we propose a framework to mine frequent largescale structures, formally ..."
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Cited by 25 (2 self)
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The problem of finding frequent patterns from graphbased datasets is an important one that finds applications in drug discovery, protein structure analysis, XML querying, and social network analysis among others. In this paper we propose a framework to mine frequent largescale structures, formally defined as frequent topological structures, from graph datasets. Key elements of our framework include, fast algorithms for discovering frequent topological patterns based on the well known notion of a topological minor, algorithms for specifying and pushing constraints deep into the mining process for discovering constrained topological patterns, and mechanisms for specifying approximate matches when discovering frequent topological patterns in noisy datasets. We demonstrate the viability and scalability of the proposed algorithms on real and synthetic datasets and also discuss the use of the framework to discover meaningful topological structures from protein structure data.
GADDI: Distance index based subgraph matching in biological networks
 In Proceedings of the 12th international conference on extending database technology (EDBT’09
, 2009
"... Currently, a huge amount of biological data can be naturally represented by graphs, e.g., protein interaction networks, gene regulatory networks, etc. The need for indexing large graphs is an urgent research problem of great practical importance. The main challenge is size. Each graph may contain ..."
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Cited by 25 (2 self)
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Currently, a huge amount of biological data can be naturally represented by graphs, e.g., protein interaction networks, gene regulatory networks, etc. The need for indexing large graphs is an urgent research problem of great practical importance. The main challenge is size. Each graph may contain thousands (or more) vertices. Most of the previous work focuses on indexing a set of small or medium sized database graphs (with only tens of vertices) and finding whether a query graph occurs in any of these. In this paper, we are interested in finding all the matches of a query graph in a given large graph of thousands of vertices, which is a very important task in many biological applications. This increases the complexity significantly. We propose a novel distance measurement which reintroduces the idea of frequent substructures in a single large graph. We devise the novel structure distance based approach (GADDI) to efficiently find matches of the query graph. GADDI is further optimized by the use of a dynamic matching scheme to minimize redundant calculations. Last but not least, a number of real and synthetic data sets are used to evaluate the efficiency and scalability of our proposed method. 1.
Maximal Biclique Subgraphs and Closed Pattern Pairs of the Adjacency Matrix: A Onetoone Correspondence and Mining Algorithms
, 2007
"... Maximal biclique (also known as complete bipartite) subgraphs can model many applications in web mining, business, and bioinformatics. Enumerating maximal biclique subgraphs from a graph is a computationally challenging problem, as the size of the output can become exponentially large with respect ..."
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Cited by 25 (8 self)
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Maximal biclique (also known as complete bipartite) subgraphs can model many applications in web mining, business, and bioinformatics. Enumerating maximal biclique subgraphs from a graph is a computationally challenging problem, as the size of the output can become exponentially large with respect to the vertex number when the graph grows. In this paper, we efficiently enumerate them through the use of closed patterns of the adjacency matrix of the graph. For an undirected graph G without selfloops, we prove that: (i) the number of closed patterns in the adjacency matrix of G is even; (ii) the number of the closed patterns is precisely double the number of maximal biclique subgraphs of G; and (iii) for every maximal biclique subgraph, there always exists a unique pair of closed patterns that matches the two vertex sets of the subgraph. Therefore, the problem of enumerating maximal bicliques can be solved by using efficient algorithms for mining closed patterns, which are algorithms extensively studied in the data mining field. However, this direct use of existing algorithms causes a duplicated enumeration. To achieve high efficiency, we propose an O(mn) time delay algorithm for a nonduplicated enumeration, in particular for enumerating those maximal bicliques with a large size, where m and n are the number of edges and vertices of the graph respectively. We evaluate the high efficiency of our algorithm by comparing it to stateoftheart algorithms on three categories of graphs: randomly generated graphs, benchmarks, and a reallife protein interaction network. In this paper, we also prove that if selfloops are allowed in a graph, then the number of closed patterns in the adjacency matrix is not necessarily even; but the maximal bicliques are exactly the same as those of the graph after removing all the selfloops.