Graph querying is the task of finding similar embeddings of a given query graph in a large target graph. Existing techniques employ the use of structural as well as node and edge label similarities to find matches of a query in the target graph. However, these techniques have ignored the presence of context (usually manifested in the form of node edge label distributions) in the query. In this paper, we propose CGQ (Contextual Graph Querying), a context-aware subgraph matching technique for querying real-world graphs. We introduce a novel sub-graph searching paradigm, which involves learning the context prevalent in the query graph. Under the proposed paradigm, we formulate the most contextually-similar subgraph querying problem that, given a query graph and a target graph, aims to identify the (top-k) maximal common subgraph(s) between the query and the target graphs with the highest contextual similarity. The quality of a match is quantized using our proposed contextual similarity function. We prove that the problem is NP-hard and also hard to approximate. Therefore, to efficiently solve the problem, we propose a hierarchical index, CGQ-Tree, with its associated search algorithm. Our experiments show that the proposed CGQ index is effective, efficient and scalable.
We present an algorithm for graph isomorphism and subgraph isomorphism suited for dealing with large graphs. A first version of the algorithm has been presented in a previous paper, where we examined its performance for the isomorphism of small and medium size graphs. The algorithm is improved here to reduce its spatial complexity and to achieve a better performance on large graphs; its features are analyzed in detail with special reference to time and memory requirements. The results of a testing performed on a publicly available database of synthetically generated graphs and on graphs relative to a real application dealing with technical drawings are presented, confirming the effectiveness of the approach, especially when working with large graphs. Complex social and information network search becomes important with a variety of applications. In the core of these applications, lies a common and critical problem: Given a labeled network and a query graph, how to efficiently search the query graph in the target network. The presence of noise and the incomplete knowledge about the structure and content of the target network make it unrealistic to find an exact match. Rather, it is more appealing to find the top-k approximate matches. In this paper, we propose a neighborhood-based similarity measure that could avoid costly graph isomorphism and edit distance computation. Under this new measure, we prove that subgraph similarity search is NP hard, while graph similarity match is polynomial. By studying the principles behind this measure, we found an information propagation model that is able to convert a large network into a set of multidimensional vectors, where sophisticated indexing and similarity search algorithms are available. The proposed method, called Ness (Neighborhood Based Similarity Search), is appropriate for graphs with low automorphism and high noise, which are common in many social and information networks. Ness is not only efficient, but also robust against structural noise and information loss. Empirical results show that it can quickly and accurately find high-quality matches in large networks, with negligible cost. Graph pattern matching is typically defined in terms of subgraph isomorphism, which makes it an np-complete problem. Moreover, it requires bijective functions, which are often too restrictive to characterize patterns in emerging applications. We propose a class of graph patterns, in which an edge denotes the connectivity in a data graph within a predefined number of hops. In addition, we define matching based on a notion of bounded simulation, an extension of graph simulation. We show that with this revision, graph pattern matching can be performed in cubic-time, by providing such an algorithm. We also develop algorithms for incrementally finding matches when data graphs are updated, with performance guarantees for dag patterns. We experimentally verify that these algorithms scale well, and that the revised notion of graph pattern matching allows us to identify communities commonly found in real-world networks. Subgraph isomorphism can be determined by means of a brute-force tree-search enumeration procedure. In this paper a new algorithm is introduced that attains efficiency by inferentially eliminating successor nodes in the tree search. To assess the time actually taken by the new algorithm, subgraph isomorphism, clique detection, graph isomorphism, and directed graph isomorphism experiments have been carried out with random and with various nonrandom graphs. A parallel asynchronous logic-in-memory implementation of a vital part of the algorithm is also described, although this hardware has not actually been built. The hardware implementation would allow very rapid determination of isomorphism. We focus on large graphs where nodes have attributes, such as a social network where the nodes are labelled with each person's job title. In such a setting, we want to find subgraphs that match a user query pattern. For example, a "star" query would be, "find a CEO who has strong interactions with a Manager, a Lawyer,and an Accountant, or another structure as close to that as possible". Similarly, a "loop" query could help spot a money laundering ring. Traditional SQL-based methods, as well as more recent graph indexing methods, will return no answer when an exact match does not exist. This is the first main feature of our method. It can find exact-, as well as near-matches, and it will present them to the user in our proposed "goodness" order. For example, our method tolerates indirect paths between, say, the "CEO" and the "Accountant" of the above sample query, when direct paths don't exist. Its second feature is scalability. In general, if the query has nq nodes and the data graph has n nodes, the problem needs polynomial time complexity O(n n q), which is prohibitive. Our G-Ray ("Graph X-Ray") method finds high-quality subgraphs in time linear on the size of the data graph. Experimental results on the DLBP author-publication graph (with 356K nodes and 1.9M edges) illustrate both the effectiveness and scalability of our approach. The results agree with our intuition, and the speed is excellent. It takes 4 seconds on average fora 4-node query on the DBLP graph. Protein–protein interactions (PPIs) and their networks play a central role in all biological processes. Akin to the complete sequencing of genomes and their comparative analysis, complete descriptions of interactomes and their comparative analysis is fundamental to a deeper understanding of biological processes. A first step in such an analysis is to align two or more PPI networks. Here, we introduce an algorithm, IsoRank, for global alignment of multiple PPI networks. The guiding intuition here is that a protein in one PPI network is a good match for a protein in another network if their respective sequences and neighborhood topologies are a good match. We encode this intuition as an eigenvalue problem in a manner analogous to Google's PageRank method. Using IsoRank, we compute a global alignment of the Saccharomyces cerevisiae, Drosophila melanogaster, Caenorhabditis elegans, Mus musculus, and Homo sapiens PPI networks. We demonstrate that incorporating PPI data in ortholog prediction results in improvements over existing sequence-only approaches and over predictions from local alignments of the yeast and fly networks. Previous methods have been effective at identifying conserved, localized network patterns across pairs of networks. This work takes the further step of performing a global alignment of multiple PPI networks. It simultaneously uses sequence similarity and network data and, unlike previous approaches, explicitly models the tradeoff inherent in combining them. We expect IsoRank—with its simultaneous handling of node similarity and network similarity—to be applicable across many scientific domains.  Due to the increasing use of RDF data, efficient processing of SPARQL queries over RDF datasets has become an important issue. However, existing solutions suffer from two limitations: 1) they cannot answer SPARQL queries with wildcards in a scalable manner; and 2) they cannot handle frequent updates in RDF repositories efficiently. Thus, most of them have to reprocess the dataset from scratch. In this paper, we propose a graph-based approach to store and query RDF data. Rather than mapping RDF triples into a relational database as most existing methods do, we store RDF data as a large graph. A SPARQL query is then converted into a corresponding subgraph matching query. In order to speed up query processing, we develop a novel index, together with some effective pruning rules and efficient search algorithms. Our method can answer exact SPARQL queries and queries with wildcards in a uniform manner. We also propose an effective maintenance algorithm to handle online updates over RDF repositories. Extensive experiments confirm the efficiency and effectiveness of our solution. It is increasingly common to find real-life data represented as networks of labeled, heterogeneous entities. To query these networks, one often needs to identify the matches of a given query graph in a (typically large) network modeled as a target graph. Due to noise and the lack of fixed schema in the target graph, the query graph can substantially differ from its matches in the target graph in both structure and node labels, thus bringing challenges to the graph querying tasks. In this paper, we propose NeMa (Network Match), a neighborhood-based subgraph matching technique for querying real-life networks. (1) To measure the quality of the match, we propose a novel subgraph matching cost metric that aggregates the costs of matching individual nodes, and unifies both structure and node label similarities. (2) Based on the metric, we formulate the minimum cost subgraph matching problem. Given a query graph and a target graph, the problem is to identify the (top-k) matches of the query graph with minimum costs in the target graph. We show that the problem is NP-hard, and also hard to approximate. (3) We propose a heuristic algorithm for solving the problem based on an inference model. In addition, we propose optimization techniques to improve the efficiency of our method. (4) We empirically verify that NeMa is both effective and efficient compared to the keyword search and various state-of-the-art graph querying techniques.  Graph pattern matching is often defined in terms of subgraph isomorphism, an np-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be conducted in cubic-time. However, they fall short of capturing the topology of data graphs, i.e., graphs may have a structure drastically different from pattern graphs they match, and the matches found are often too large to understand and analyze. To rectify these problems, this paper proposes a notion of strong simulation, a revision of graph simulation, for graph pattern matching. (1) We identify a set of criteria for preserving the topology of graphs matched. We show that strong simulation preserves the topology of data graphs and finds a bounded number of matches. (2) We show that strong simulation retains the same complexity as earlier extensions of simulation, by providing a cubic-time algorithm for computing strong simulation. (3) We present the locality property of strong simulation, which allows us to effectively conduct pattern matching on distributed graphs. (4) We experimentally verify the effectiveness and efficiency of these algorithms, using real-life data and synthetic data. Large graph datasets are common in many emerging database applications, and most notably in large-scale scientific applications. To fully exploit the wealth of information encoded in graphs, effective and efficient graph matching tools are critical. Due to the noisy and incomplete nature of real graph datasets, approximate, rather than exact, graph matching is required. Furthermore, many modern applications need to query large graphs, each of which has hundreds to thousands of nodes and edges. This paper presents a novel technique for approximate matching of large graph queries. We propose a novel indexing method that incorporates graph structural information in a hybrid index structure. This indexing technique achieves high pruning power and the index size scales linearly with the database size. In addition, we propose an innovative matching paradigm to query large graphs. This technique distinguishes nodes by their importance in the graph structure. The matching algorithm first matches the important nodes of a query and then progressively extends these matches. Through experiments on several real datasets, this paper demonstrates the effectiveness and efficiency of the proposed method. Motivation: With the rapid increase in the availability of biological graph datasets, there is a growing need for effective and efficient graph querying methods. Due to the noisy and incomplete characteristics of these datasets, exact graph matching methods have limited use and approximate graph matching methods are required. Unfortunately, existing graph matching methods are too restrictive as they only allow exact or near exact graph matching. This paper presents a novel approximate graph matching technique called SAGA. This technique employs a flexible model for computing graph similarity, which allows for node gaps, node mismatches and graph structural differences. SAGA employs an indexing technique that allows it to efficiently evaluate queries even against large graph datasets. Results: SAGA has been used to query biological pathways and literature datasets, which has revealed interesting similarities between distinct pathways that cannot be found by existing methods. These matches associate seemingly unrelated biological processes, connect studies in different sub-areas of biomedical research and thus pose hypotheses for new discoveries. SAGA is also orders of magnitude faster than existing methods. Availability: SAGA can be accessed freely via the web at http: www.eecs.umich.edu saga. Binaries are also freely available at this website. Contact: jignesh@eecs.umich.edu Supplementary material: Supplementary material is available at http: www.eecs.umich.edu periscope publ saga-suppl.pdf. Finding subgraph isomorphisms is an important problem in many applications which deal with data modeled as graphs. While this problem is NP-hard, in recent years, many algorithms have been proposed to solve it in a reasonable time for real datasets using different join orders, pruning rules, and auxiliary neighborhood information. However, since they have not been empirically compared one another in most research work, it is not clear whether the later work outperforms the earlier work. Another problem is that reported comparisons were often done using the original authors' binaries which were written in different programming environments. In this paper, we address these serious problems by re-implementing five state-of-the-art subgraph isomorphism algorithms in a common code base and by comparing them using many real-world datasets and their query loads. Through our in-depth analysis of experimental results, we report surprising empirical findings.