An introduction to Graph Data Management

A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type constructors. In this article we present the basic notions of graph databases, give an historical overview of its main development, and study the main current systems that implement them

Graphs, Matrices, and the GraphBLAS: Seven Good Reasons

The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical complexity, (5) theoretical analysis, (6) serial performance, and (7) parallel performance. Implementing graph algorithms using matrix-based approaches provides a number of promising solutions to these challenges. The GraphBLAS standard (istc- bigdata.org/GraphBlas) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. The GraphBLAS mathematically defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the GraphBLAS and describes how the GraphBLAS can be used to address many of the challenges associated with analysis of graphs.Comment: 10 pages; International Conference on Computational Science workshop on the Applications of Matrix Computational Methods in the Analysis of Modern Dat

Searching for the Causal Structure of a Vector Autoregression

Vector autoregressions (VARs) are economically interpretable only when identified by being transformed into a structural form (the SVAR) in which the contemporaneous variables stand in a well-defined causal order. These identifying transformations are not unique. It is widely believed that practitioners must choose among them using a priori theory or other criteria not rooted in the data under analysis. We show how to apply graph-theoretic methods of searching for causal structure based on relations of conditional independence to select among the possible causal orders – or at least to reduce the admissible causal orders to a narrow equivalence class. The graph-theoretic approaches were developed by computer scientists and philosophers (Pearl, Glymour, Spirtes among others) and applied to cross-sectional data. We provide an accessible introduction to this work. Then building on the work of Swanson and Granger (1997), we show how to apply it to searching for the causal order of an SVAR. We present simulation results to show how the efficacy of the search method algorithm varies with signal strength for realistic sample lengths. Our findings suggest that graph-theoretic methods may prove to be a useful tool in the analysis of SVARs.search, causality, structural vector autoregression, graph theory, common cause, causal Markov condition, Wold causal order, identification; PC algorithm

A General Introduction To Graph Visualization Techniques

Generally, a graph is an abstract data type used to represent relations among a given set of data entities. Graphs are used in numerous applications within the field of information visualization, such as VLSI (circuit schematics), state-transition diagrams, and social networks. The size and complexity of graphs easily reach dimensions at which the task of exploring and navigating gets crucial. Moreover, additional requirements have to be met in order to provide proper visualizations. In this context, many techniques already have been introduced. This survey aims to provide an introduction on graph visualization techniques helping the reader to gain a first insight into the most fundamental techniques. Furthermore, a brief introduction about navigation and interaction tools is provided

A spatial signature of sprawl: or the proportion and distribution of linear networkcircuits

This paper sets out to investigate whether the frequency distribution ofthe linear network circuits within a graph-based representation of aroad transportation system can be helpful in identifying sprawl and, inparticular, whether a 'spatial signature of sprawl' can be determined.This paper is based upon an earlier study on Peachtree City, Georgia and in particular of its dual transportation system (roads and golf cartpaths). In order to fully understand the effect that the dualtransportation system has upon Peachtree City, the frequencydistribution of its circuits are compared to three, supposed, 'suburban' areas and three, supposed, 'urban' districts. The conclusion of thispaper is that there is, unquestionably, a measurable continuum between 'suburbia' and 'urbanity' and that this is reflected in the frequency,length and distribution of the graph network circuits. The main sectionof this paper is concerned with the presentation and discussion ofalternative algorithms for calculating these circuits. This section isfollowed by an introduction of a selection of methods for interpretingthe resultant data. Finally, with respect to Peachtree City, this paperconcludes that the effect of the dual transportation system is to make it more 'urban' than it would otherwise be, although it remains adistinctly suburban environment

Sequential Patterns Post-processing for Structural Relation Patterns Mining

Sequential patterns mining is an important data-mining technique used to identify frequently observed sequential occurrence of items across ordered transactions over time. It has been extensively studied in the literature, and there exists a diversity of algorithms. However, more complex structural patterns are often hidden behind sequences. This article begins with the introduction of a model for the representation of sequential patterns—Sequential Patterns Graph—which motivates the search for new structural relation patterns. An integrative framework for the discovery of these patterns–Postsequential Patterns Mining–is then described which underpins the postprocessing of sequential patterns. A corresponding data-mining method based on sequential patterns postprocessing is proposed and shown to be effective in the search for concurrent patterns. From experiments conducted on three component algorithms, it is demonstrated that sequential patterns-based concurrent patterns mining provides an efficient method for structural knowledge discover