Janusz J. Charatonik, Krzysztof Omiljanowski, Biagio Ricceri · SHILAP Revista de lepidopterología · 1992
<p style="font-style: normal;"><span style="font-family: DejaVu Sans,sans-serif;">A pair <em>(X,Y) </em>of topological spaces X and Y<em> </em>is said to have the graph intersection property provided that for each continuous function <em>g: XY</em>, if a connected subset of<em> X Y </em>projects onto the whole <em>Y</em>, then it intersect the graph of <em>g</em>. Various relations between this and other known properties related to mapping theory are studied.</span> <p style="font-style: normal;"><span style="font-family: DejaVu Sans,sans-serif;">In particular, it is proved that: 1) if a space <em>X</em> is completely regular and a space <em>Y </em>is an arcwise connected metric continuum distinct from an arc, then the pair <em>(X,Y)</em> has the graph intersection property if and only if <em>X</em> is hereditary disconnected; 2) if a connected space <em>Y</em> is fixed, then the graph intersection property holds for every pair <em>(X,Y)</em> if and only if there is a closed linear order on <em>Y</em> with minimal and maximal elements. Related results are obtained.</span>
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Noga Alon, Joel Spencer · 2008
This chapter contains sections titled: Property Testing Testing Colorability Szemerédi's Regularity Lemma Testing Triangle-Freeness Characterizing the Testable Graph Properties Exercises The Probabilistic Lens: Turán Numbers and Dependent Random Choice
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Lovász, László, Vesztergombi, Katalin · arXiv (Cornell University) · 2012
A property of finite graphs is called nondeterministically testable if it has a "certificate" such that once the certificate is specified, its correctness can be verified by random local testing. In this paper we study certificates that consist of one or more unary and/or binary relations on the nodes, in the case of dense graphs. Using the theory of graph limits, we prove that nondeterministically testable properties are also deterministically testable.
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Colombo, Andrea, Bernasconi, Anna, Ceri, Stefano · Zenodo (CERN European Organization for Nuclear Research) · 2024
Property Graph for the Italian legislative system that we presented in the paper Modelling Legislative Systems into Property Graphs to Enable Advanced Pattern Detection submitted to CIKM 2024 - Applied Research
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H. Shank · Theory of Computing Systems · 1971
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Hirokazu Chiba, Ryota Yamanaka, Shota Matsumoto · arXiv (Cornell University) · 2019
Recently, a variety of database implementations adopting the property graph model have emerged. However, interoperable management of graph data on these implementations is challenging due to the differences in data models and formats. Here, we redefine the property graph model incorporating the differences in the existing models and propose interoperable serialization formats for property graphs. The model is independent of specific implementations and provides a basis of interoperable management of property graph data. The proposed serialization is not only general but also intuitive, thus it is useful for creating and maintaining graph data. To demonstrate the practical use of our model and serialization, we implemented converters from our serialization into existing formats, which can then be loaded into various graph databases. This work provides a basis of an interoperable platform for creating, exchanging, and utilizing property graph data.
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Larissa C. Shimomura, Nikolay Yakovets, George Fletcher · 2024
Knowledge graphs have soared in popularity by supporting different types of applications and domains. In this context, the property graph data model has become an emerging standard in industry and academia. With its widespread use, there is also an increasing interest in investigating constraints for property graph data and their applications in data profiling. Graph Generating Dependencies (GGDs) are a class of property graph data dependencies that can express constraints on topology and properties of nodes and edges of the graph, making them a suitable candidate to expose an overview of the property graph to the user (profile graph data). However, GGDs can be difficult to set manually. To solve this issue, we propose a framework for discovering GGDs automatically from the property graph to profile graph data. Our framework has three main steps: (1) pre-processing, (2) candidate generation, and, (3) GGD extraction. Our results show that the discovered set of GGDs can give an overview of the input graph, including schema-level information between the graph patterns and attributes.
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Larissa C. Shimomura, Nikolay Yakovets, George Fletcher · arXiv (Cornell University) · 2024
With the increasing use of graph-structured data, there is also increasing interest in investigating graph data dependencies and their applications, e.g., in graph data profiling. Graph Generating Dependencies (GGDs) are a class of dependencies for property graphs that can express the relation between different graph patterns and constraints based on their attribute similarities. Rich syntax and semantics of GGDs make them a good candidate for graph data profiling. Nonetheless, GGDs are difficult to define manually, especially when there are no data experts available. In this paper, we propose GGDMiner, a framework for discovering approximate GGDs from graph data automatically, with the intention of profiling graph data through GGDs for the user. GGDMiner has three main steps: (1) pre-processing, (2) candidate generation, and, (3) GGD extraction. To optimize memory consumption and execution time, GGDMiner uses a factorized representation of each discovered graph pattern, called Answer Graph. Our results show that the discovered set of GGDs can give an overview about the input graph, both schema level information and also correlations between the graph patterns and attributes.
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Walter Kropatsch · 1998
this paper we show a computational solution that needs less complex computations. In our case one computation stage consists in a transformation
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Andrea Bianchi, Adela Yiyu Zhang · arXiv (Cornell University) · 2026
We exhibit the symmetric monoidal $\infty$-category $\mathrm{GrCob}$ of graph cobordisms between spaces as a full $\infty$-subcategory of the $\infty$-category $\mathrm{Psh}(\mathrm{Gr})$ of presheaves over $\mathrm{Gr}$, where $\mathrm{Gr}$ is the symmetric monoidal $\infty$-category of graph cobordisms between finite sets. We also describe a universal property for $\mathrm{GrCob}$: it is, in a suitable sense, the free symmetric monoidal extension of $\mathrm{Gr}$ endowed with the factorization homology $\int_X*$ of the universal $\mathbf{E}_\infty$-Frobenius algebra for all spaces $X$. As a corollary, we identify the space of universal natural operations on the factorization homologies, in particular the Hochschild homology, of $\mathbf{E}_\infty$-Frobenius algebras.
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Chiba, Hirokazu, Voß, Jakob · Zenodo (CERN European Organization for Nuclear Research) · 2024
This document specifies a common data model of labeled property graphs, a syntax to write property graphs in a compact textual form, and serialization formats of property graphs in JSON and in newline-delimited JSON.
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Warren, Paul · Figshare · 2020
Handout describing the basic features of Cypher used in a usability study of Property Graphs. Provides an overview of the basic features of the Cypher language.<br>The aim of the study is to understand the difficulties people experience with graph database languages; and to understand their preferences in data modelling. Cypher is taken as an example of query languages used for property graphs.<br>There is a parallel study looking at RDF* and SPARQL*, and another aim of the work is to compare people's behaviour with the two classes of languages.<br>The study is currently in progress. When complete, the results will be published in the research literature.
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Andrea Bianchi, Adela Yiyu Zhang · ArXiv.org · 2026
We exhibit the symmetric monoidal $\infty$-category $\mathrm{GrCob}$ of graph cobordisms between spaces as a full $\infty$-subcategory of the $\infty$-category $\mathrm{Psh}(\mathrm{Gr})$ of presheaves over $\mathrm{Gr}$, where $\mathrm{Gr}$ is the symmetric monoidal $\infty$-category of graph cobordisms between finite sets. We also describe a universal property for $\mathrm{GrCob}$: it is, in a suitable sense, the free symmetric monoidal extension of $\mathrm{Gr}$ endowed with the factorization homology $\int_X*$ of the universal $\mathbf{E}_\infty$-Frobenius algebra for all spaces $X$. As a corollary, we identify the space of universal natural operations on the factorization homologies, in particular the Hochschild homology, of $\mathbf{E}_\infty$-Frobenius algebras.
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Colombo, Andrea · Zenodo (CERN European Organization for Nuclear Research) · 2025
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Warren, Paul · Open Research Online (The Open University) · 2020
Handout describing the basic features of Cypher used in a usability study of Property Graphs. Provides an overview of the basic features of the Cypher language.<br>The aim of the study is to understand the difficulties people experience with graph database languages; and to understand their preferences in data modelling. Cypher is taken as an example of query languages used for property graphs.<br>There is a parallel study looking at RDF* and SPARQL*, and another aim of the work is to compare people's behaviour with the two classes of languages.<br>The study is currently in progress. When complete, the results will be published in the research literature.
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Michał Adamaszek · Discussiones Mathematicae Graph Theory · 2014
A property of n-vertex graphs is called evasive if every algorithm testing this property by asking questions of the form "is there an edge between vertices u and v" requires, in the worst case, to ask about all pairs of vertices. Most "natural" graph properties are either evasive or conjectured to be such, and of the few examples of nontrivial nonevasive properties scattered in the literature the smallest one has n = 6.
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Noga Alon, A. Shapira · Algorithms and combinatorics · 2007
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Amedeo Pachera, Angela Bonifati, Andrea Mauri · Proceedings of the ACM on Management of Data · 2025
Property graphs serve as unifying abstractions for encoding, inspecting, and updating interconnected data with greater expressive power. They are increasingly popular across various application domains involving real users. However, graph data often contains inconsistencies that need proper transformations to address underlying constraint violations and often require specific domain knowledge. In this paper, we propose an interactive and user-centric approach to repair property graphs under denial constraints. Our approach includes a novel theoretical framework comprising a query-based inconsistency detection mechanism, a dependency graph for tracking violations, and an assignment algorithm facilitating multi-user property graph repairs by leveraging independent sets. We evaluate our approach through several experiments on real-world and synthetic datasets, considering different levels of user expertise and comparing against various baselines. Even with multiple non-oracle users, our approach outperforms existing interactive and non-interactive baselines by 30% on average in terms of repair quality. Additionally, we conduct a user study to assess real user performance in property graph repairs.
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Kaidi Cao, Phitchaya Mangpo Phothilimthana, Sami Abu-El-Haija et al. · arXiv (Cornell University) · 2023
Learning to predict properties of large graphs is challenging because each prediction requires the knowledge of an entire graph, while the amount of memory available during training is bounded. Here we propose Graph Segment Training (GST), a general framework that utilizes a divide-and-conquer approach to allow learning large graph property prediction with a constant memory footprint. GST first divides a large graph into segments and then backpropagates through only a few segments sampled per training iteration. We refine the GST paradigm by introducing a historical embedding table to efficiently obtain embeddings for segments not sampled for backpropagation. To mitigate the staleness of historical embeddings, we design two novel techniques. First, we finetune the prediction head to fix the input distribution shift. Second, we introduce Stale Embedding Dropout to drop some stale embeddings during training to reduce bias. We evaluate our complete method GST-EFD (with all the techniques together) on two large graph property prediction benchmarks: MalNet and TpuGraphs. Our experiments show that GST-EFD is both memory-efficient and fast, while offering a slight boost on test accuracy over a typical full graph training regime.
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Sami Abu-El-Haija, Kaidi Cao, Jure Leskovec et al. · 2023
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