Graph Databases for Beginners Bryce Merkl Sasaki, Joy Chao & Rachel Howard
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1. Directed Graphs Or Quivers What Is Category Theory? • Graph Theory on Steroids • Comic Book Mathematics • Abstract Nonsense • the Secret Dictionary
1. Directed graphs or quivers What is category theory? • Graph theory on steroids • Comic book mathematics • Abstract nonsense • The secret dictionary Sets and classes: For S = fX j X2 = Xg, have S 2 S , S2 = S Directed graph or quiver: C = (C0;C1;@0 : C1 ! C0;@1 : C1 ! C0) Class C0 of objects, vertices, points, . Class C1 of morphisms, (directed) edges, arrows, . For x; y 2 C0, write C(x; y) := ff 2 C1 j @0f = x; @1f = yg f 2C1 tail, domain / @0f / @1f o head, codomain op Opposite or dual graph of C = (C0;C1;@0;@1) is C = (C0;C1;@1;@0) Graph homomorphism F : D ! C has object part F0 : D0 ! C0 and morphism part F1 : D1 ! C1 with @i ◦ F1(f) = F0 ◦ @i(f) for i = 0; 1. Graph isomorphism has bijective object and morphism parts. Poset (X; ≤): set X with reflexive, antisymmetric, transitive order ≤ Hasse diagram of poset (X; ≤): x ! y if y covers x, i.e., x 6= y and [x; y] = fx; yg, so x ≤ z ≤ y ) z = x or z = y. Hasse diagram of (N; ≤) is 0 / 1 / 2 / 3 / ::: Hasse diagram of (f1; 2; 3; 6g; j ) is 3 / 6 O O 1 / 2 1 2 2. Categories Category: Quiver C = (C0;C1;@0 : C1 ! C0;@1 : C1 ! C0) with: • composition: 8 x; y; z 2 C0 ; C(x; y) × C(y; z) ! C(x; z); (f; g) 7! g ◦ f • satisfying associativity: 8 x; y; z; t 2 C0 ; 8 (f; g; h) 2 C(x; y) × C(y; z) × C(z; t) ; h ◦ (g ◦ f) = (h ◦ g) ◦ f y iS qq <SSSS g qq << SSS f qqq h◦g < SSSS qq << SSS qq g◦f < SSS xqq << SS z Vo VV < x VVVV << VVVV < VVVV << h VVVV < h◦(g◦f)=(h◦g)◦f VVVV < VVV+ t • identities: 8 x; y; z 2 C0 ; 9 1y 2 C(y; y) : 8 f 2 C(x; y) ; 1y ◦ f = f and 8 g 2 C(y; z) ; g ◦ 1y = g f y o x MM MM 1y g MM MMM f MMM M& zo g y Example: N0 = fxg ; N1 = N ; 1x = 0 ; 8 m; n 2 N ; n◦m = m+n ; | one object, lots of arrows [monoid of natural numbers under addition] 4 x / x Equation: 3 + 5 = 4 + 4 Commuting diagram: 3 4 x / x 5 ( 1 if m ≤ n; Example: N1 = N ; 8 m; n 2 N ; jN(m; n)j = 0 otherwise | lots of objects, lots of arrows [poset (N; ≤) as a category] These two examples are small categories: have a set of morphisms. -
Empirical Study on the Usage of Graph Query Languages in Open Source Java Projects
Empirical Study on the Usage of Graph Query Languages in Open Source Java Projects Philipp Seifer Johannes Härtel Martin Leinberger University of Koblenz-Landau University of Koblenz-Landau University of Koblenz-Landau Software Languages Team Software Languages Team Institute WeST Koblenz, Germany Koblenz, Germany Koblenz, Germany [email protected] [email protected] [email protected] Ralf Lämmel Steffen Staab University of Koblenz-Landau University of Koblenz-Landau Software Languages Team Koblenz, Germany Koblenz, Germany University of Southampton [email protected] Southampton, United Kingdom [email protected] Abstract including project and domain specific ones. Common applica- Graph data models are interesting in various domains, in tion domains are management systems and data visualization part because of the intuitiveness and flexibility they offer tools. compared to relational models. Specialized query languages, CCS Concepts • General and reference → Empirical such as Cypher for property graphs or SPARQL for RDF, studies; • Information systems → Query languages; • facilitate their use. In this paper, we present an empirical Software and its engineering → Software libraries and study on the usage of graph-based query languages in open- repositories. source Java projects on GitHub. We investigate the usage of SPARQL, Cypher, Gremlin and GraphQL in terms of popular- Keywords Empirical Study, GitHub, Graphs, Query Lan- ity and their development over time. We select repositories guages, SPARQL, Cypher, Gremlin, GraphQL based on dependencies related to these technologies and ACM Reference Format: employ various popularity and source-code based filters and Philipp Seifer, Johannes Härtel, Martin Leinberger, Ralf Lämmel, ranking features for a targeted selection of projects. -
Graph Database for Collaborative Communities Rania Soussi, Marie-Aude Aufaure, Hajer Baazaoui
Graph Database for Collaborative Communities Rania Soussi, Marie-Aude Aufaure, Hajer Baazaoui To cite this version: Rania Soussi, Marie-Aude Aufaure, Hajer Baazaoui. Graph Database for Collaborative Communities. Community-Built Databases, Springer, pp.205-234, 2011. hal-00708222 HAL Id: hal-00708222 https://hal.archives-ouvertes.fr/hal-00708222 Submitted on 14 Jun 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Graph Database For collaborative Communities 1, 2 1 Rania Soussi , Marie-Aude Aufaure , Hajer Baazaoui2 1Ecole Centrale Paris, Applied Mathematics & Systems Laboratory (MAS), SAP Business Objects Academic Chair in Business Intelligence 2Riadi-GDL Laboratory, ENSI – Manouba University, Tunis Abstract Data manipulated in an enterprise context are structured data as well as un- structured data such as emails, documents, social networks, etc. Graphs are a natural way of representing and modeling such data in a unified manner (Structured, semi-structured and unstructured ones). The main advantage of such a structure relies in the dynamic aspect and the capability to represent relations, even multiple ones, between objects. Recent database research work shows a growing interest in the definition of graph models and languages to allow a natural way of handling data appearing. -
Semantics Developer's Guide
MarkLogic Server Semantic Graph Developer’s Guide 2 MarkLogic 10 May, 2019 Last Revised: 10.0-8, October, 2021 Copyright © 2021 MarkLogic Corporation. All rights reserved. MarkLogic Server MarkLogic 10—May, 2019 Semantic Graph Developer’s Guide—Page 2 MarkLogic Server Table of Contents Table of Contents Semantic Graph Developer’s Guide 1.0 Introduction to Semantic Graphs in MarkLogic ..........................................11 1.1 Terminology ..........................................................................................................12 1.2 Linked Open Data .................................................................................................13 1.3 RDF Implementation in MarkLogic .....................................................................14 1.3.1 Using RDF in MarkLogic .........................................................................15 1.3.1.1 Storing RDF Triples in MarkLogic ...........................................17 1.3.1.2 Querying Triples .......................................................................18 1.3.2 RDF Data Model .......................................................................................20 1.3.3 Blank Node Identifiers ..............................................................................21 1.3.4 RDF Datatypes ..........................................................................................21 1.3.5 IRIs and Prefixes .......................................................................................22 1.3.5.1 IRIs ............................................................................................22 -
Graph Theory
1 Graph Theory “Begin at the beginning,” the King said, gravely, “and go on till you come to the end; then stop.” — Lewis Carroll, Alice in Wonderland The Pregolya River passes through a city once known as K¨onigsberg. In the 1700s seven bridges were situated across this river in a manner similar to what you see in Figure 1.1. The city’s residents enjoyed strolling on these bridges, but, as hard as they tried, no residentof the city was ever able to walk a route that crossed each of these bridges exactly once. The Swiss mathematician Leonhard Euler learned of this frustrating phenomenon, and in 1736 he wrote an article [98] about it. His work on the “K¨onigsberg Bridge Problem” is considered by many to be the beginning of the field of graph theory. FIGURE 1.1. The bridges in K¨onigsberg. J.M. Harris et al., Combinatorics and Graph Theory , DOI: 10.1007/978-0-387-79711-3 1, °c Springer Science+Business Media, LLC 2008 2 1. Graph Theory At first, the usefulness of Euler’s ideas and of “graph theory” itself was found only in solving puzzles and in analyzing games and other recreations. In the mid 1800s, however, people began to realize that graphs could be used to model many things that were of interest in society. For instance, the “Four Color Map Conjec- ture,” introduced by DeMorgan in 1852, was a famous problem that was seem- ingly unrelated to graph theory. The conjecture stated that four is the maximum number of colors required to color any map where bordering regions are colored differently. -
An Application of Graph Theory in Markov Chains Reliability Analysis
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by DSpace at VSB Technical University of Ostrava STATISTICS VOLUME: 12 j NUMBER: 2 j 2014 j JUNE An Application of Graph Theory in Markov Chains Reliability Analysis Pavel SKALNY Department of Applied Mathematics, Faculty of Electrical Engineering and Computer Science, VSB–Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava-Poruba, Czech Republic [email protected] Abstract. The paper presents reliability analysis which the production will be equal or greater than the indus- was realized for an industrial company. The aim of the trial partner demand. To deal with the task a Monte paper is to present the usage of discrete time Markov Carlo simulation of Discrete time Markov chains was chains and the flow in network approach. Discrete used. Markov chains a well-known method of stochastic mod- The goal of this paper is to present the Discrete time elling describes the issue. The method is suitable for Markov chain analysis realized on the system, which is many systems occurring in practice where we can easily not distributed in parallel. Since the analysed process distinguish various amount of states. Markov chains is more complicated the graph theory approach seems are used to describe transitions between the states of to be an appropriate tool. the process. The industrial process is described as a graph network. The maximal flow in the network cor- Graph theory has previously been applied to relia- responds to the production. The Ford-Fulkerson algo- bility, but for different purposes than we intend. -
RDF Query Languages Need Support for Graph Properties
RDF Query Languages Need Support for Graph Properties Renzo Angles1, Claudio Gutierrez1, and Jonathan Hayes1,2 1 Dept. of Computer Science, Universidad de Chile 2 Dept. of Computer Science, Technische Universit¨at Darmstadt, Germany {rangles,cgutierr,jhayes}@dcc.uchile.cl Abstract. This short paper discusses the need to include into RDF query languages the ability to directly query graph properties from RDF data. We study the support that current RDF query languages give to these features, to conclude that they are currently not supported. We propose a set of basic graph properties that should be added to RDF query languages and provide evidence for this view. 1 Introduction One of the main features of the Resource Description Framework (RDF) is its ability to interconnect information resources, resulting in a graph-like structure for which connectivity is a central notion [GLMB98]. As we will argue, basic concepts of graph theory such as degree, path, and diameter play an important role for applications that involve RDF querying. Considering the fact that the data model influences the set of operations that should be provided by a query language [HBEV04], it follows the need for graph operations support in RDF query languages. For example, the query “all relatives of degree 1 of Alice”, submitted to a genealogy database, amounts to retrieving the nodes adjacent to a resource. The query “are suspects A and B related?”, submitted to a police database, asks for any path connecting these resources in the (RDF) graph that is stored in this database. The query “what is the Erd˝osnumber of Alberto Mendelzon”, submitted to (a RDF version of) DBLP, asks simply for the length of the shortest path between the nodes representing Erd˝osand Mendelzon. -
Property Graph Vs RDF Triple Store: a Comparison on Glycan Substructure Search
RESEARCH ARTICLE Property Graph vs RDF Triple Store: A Comparison on Glycan Substructure Search Davide Alocci1,2, Julien Mariethoz1, Oliver Horlacher1,2, Jerven T. Bolleman3, Matthew P. Campbell4, Frederique Lisacek1,2* 1 Proteome Informatics Group, SIB Swiss Institute of Bioinformatics, Geneva, 1211, Switzerland, 2 Computer Science Department, University of Geneva, Geneva, 1227, Switzerland, 3 Swiss-Prot Group, SIB Swiss Institute of Bioinformatics, Geneva, 1211, Switzerland, 4 Department of Chemistry and Biomolecular Sciences, Macquarie University, Sydney, Australia * [email protected] Abstract Resource description framework (RDF) and Property Graph databases are emerging tech- nologies that are used for storing graph-structured data. We compare these technologies OPEN ACCESS through a molecular biology use case: glycan substructure search. Glycans are branched Citation: Alocci D, Mariethoz J, Horlacher O, tree-like molecules composed of building blocks linked together by chemical bonds. The Bolleman JT, Campbell MP, Lisacek F (2015) molecular structure of a glycan can be encoded into a direct acyclic graph where each node Property Graph vs RDF Triple Store: A Comparison on Glycan Substructure Search. PLoS ONE 10(12): represents a building block and each edge serves as a chemical linkage between two build- e0144578. doi:10.1371/journal.pone.0144578 ing blocks. In this context, Graph databases are possible software solutions for storing gly- Editor: Manuela Helmer-Citterich, University of can structures and Graph query languages, such as SPARQL and Cypher, can be used to Rome Tor Vergata, ITALY perform a substructure search. Glycan substructure searching is an important feature for Received: July 16, 2015 querying structure and experimental glycan databases and retrieving biologically meaning- ful data. -
Application of Graph Databases for Static Code Analysis of Web-Applications
Application of Graph Databases for Static Code Analysis of Web-Applications Daniil Sadyrin [0000-0001-5002-3639], Andrey Dergachev [0000-0002-1754-7120], Ivan Loginov [0000-0002-6254-6098], Iurii Korenkov [0000-0002-8948-2776], and Aglaya Ilina [0000-0003-1866-7914] ITMO University, Kronverkskiy prospekt, 49, St. Petersburg, 197101, Russia [email protected], [email protected], [email protected], [email protected], [email protected] Abstract. Graph databases offer a very flexible data model. We present the approach of static code analysis using graph databases. The main stage of the analysis algorithm is the construction of ASG (Abstract Source Graph), which represents relationships between AST (Abstract Syntax Tree) nodes. The ASG is saved to a graph database (like Neo4j) and queries to the database are made to get code properties for analysis. The approach is applied to detect and exploit Object Injection vulnerability in PHP web-applications. This vulnerability occurs when unsanitized user data enters PHP unserialize function. Successful exploitation of this vulnerability means building of “object chain”: a nested object, in the process of deserializing of it, a sequence of methods is being called leading to dangerous function call. In time of deserializing, some “magic” PHP methods (__wakeup or __destruct) are called on the object. To create the “object chain”, it’s necessary to analyze methods of classes declared in web-application, and find sequence of methods called from “magic” methods. The main idea of author’s approach is to save relationships between methods and functions in graph database and use queries to the database on Cypher language to find appropriate method calls. -
Database Software Market: Billy Fitzsimmons +1 312 364 5112
Equity Research Technology, Media, & Communications | Enterprise and Cloud Infrastructure March 22, 2019 Industry Report Jason Ader +1 617 235 7519 [email protected] Database Software Market: Billy Fitzsimmons +1 312 364 5112 The Long-Awaited Shake-up [email protected] Naji +1 212 245 6508 [email protected] Please refer to important disclosures on pages 70 and 71. Analyst certification is on page 70. William Blair or an affiliate does and seeks to do business with companies covered in its research reports. As a result, investors should be aware that the firm may have a conflict of interest that could affect the objectivity of this report. This report is not intended to provide personal investment advice. The opinions and recommendations here- in do not take into account individual client circumstances, objectives, or needs and are not intended as recommen- dations of particular securities, financial instruments, or strategies to particular clients. The recipient of this report must make its own independent decisions regarding any securities or financial instruments mentioned herein. William Blair Contents Key Findings ......................................................................................................................3 Introduction .......................................................................................................................5 Database Market History ...................................................................................................7 Market Definitions -
Graph Algorithms in Bioinformatics an Introduction to Bioinformatics Algorithms Outline
An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Graph Algorithms in Bioinformatics An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Outline 1. Introduction to Graph Theory 2. The Hamiltonian & Eulerian Cycle Problems 3. Basic Biological Applications of Graph Theory 4. DNA Sequencing 5. Shortest Superstring & Traveling Salesman Problems 6. Sequencing by Hybridization 7. Fragment Assembly & Repeats in DNA 8. Fragment Assembly Algorithms An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Section 1: Introduction to Graph Theory An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Knight Tours • Knight Tour Problem: Given an 8 x 8 chessboard, is it possible to find a path for a knight that visits every square exactly once and returns to its starting square? • Note: In chess, a knight may move only by jumping two spaces in one direction, followed by a jump one space in a perpendicular direction. http://www.chess-poster.com/english/laws_of_chess.htm An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 9th Century: Knight Tours Discovered An Introduction to Bioinformatics Algorithms www.bioalgorithms.info 18th Century: N x N Knight Tour Problem • 1759: Berlin Academy of Sciences proposes a 4000 francs prize for the solution of the more general problem of finding a knight tour on an N x N chessboard. • 1766: The problem is solved by Leonhard Euler (pronounced “Oiler”). • The prize was never awarded since Euler was Director of Mathematics at Berlin Academy and was deemed ineligible. Leonhard Euler http://commons.wikimedia.org/wiki/File:Leonhard_Euler_by_Handmann.png An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Introduction to Graph Theory • A graph is a collection (V, E) of two sets: • V is simply a set of objects, which we call the vertices of G. -
Web and Semantic Web Query Languages: a Survey
Web and Semantic Web Query Languages: A Survey James Bailey1, Fran¸coisBry2, Tim Furche2, and Sebastian Schaffert2 1 NICTA Victoria Laboratory Department of Computer Science and Software Engineering The University of Melbourne, Victoria 3010, Australia http://www.cs.mu.oz.au/~jbailey/ 2 Institute for Informatics,University of Munich, Oettingenstraße 67, 80538 M¨unchen, Germany http://pms.ifi.lmu.de/ Abstract. A number of techniques have been developed to facilitate powerful data retrieval on the Web and Semantic Web. Three categories of Web query languages can be distinguished, according to the format of the data they can retrieve: XML, RDF and Topic Maps. This ar- ticle introduces the spectrum of languages falling into these categories and summarises their salient aspects. The languages are introduced us- ing common sample data and query types. Key aspects of the query languages considered are stressed in a conclusion. 1 Introduction The Semantic Web Vision A major endeavour in current Web research is the so-called Semantic Web, a term coined by W3C founder Tim Berners-Lee in a Scientific American article describing the future of the Web [37]. The Semantic Web aims at enriching Web data (that is usually represented in (X)HTML or other XML formats) by meta-data and (meta-)data processing specifying the “meaning” of such data and allowing Web based systems to take advantage of “intelligent” reasoning capabilities. To quote Berners-Lee et al. [37]: “The Semantic Web will bring structure to the meaningful content of Web pages, creating an environment where software agents roaming from page to page can readily carry out sophisticated tasks for users.” The Semantic Web meta-data added to today’s Web can be seen as advanced semantic indices, making the Web into something rather like an encyclopedia.