The Global Urban Graph dataset provides pre-computed urban graphs that can be converted into NetworkX, igraph, PyG, and DGL graph formats.Each .zip folder contains the node and edge information required to construct a full-scale city graph. This consists of graph nodes and their features (plots, buildings, streets, and intersections) and connections between nodes. To support robustness to diverse urban applications, we do not instantiate graph edges directly. Instead, users can specify how they wish to construct graph edges (e.g. by k-nearest neighbour or Euclidean distance). These functionalities have been implemented with the Urbanity python package which provides functionalities for saving, loading, visualising, processing, and converting urban graphs to machine learning friendly formats (PyG and DGL). Installation instructions are available at: https://github.com/winstonyym/urbanityThe graphs are referenced to global coordinate reference system (EPSG:4326). If you have any questions, please email: winstonyym@u.nus.edu / winyap@mit.edu

Numerous types of real-world data can be naturally represented as graphs, such as social networks, trading networks, and biological molecules. This highlights the need for effective graph representations to support various tasks. In recent years, graph neural networks (GNNs) have demonstrated remarkable success in extracting information from graphs and enabling graph-related tasks. However, they still face a series of challenges in solving real-world problems, including scarcity of labeled data, scalability issues, potential bias, etc. These challenges stem from both domain-specific issues and inherent limitations of GNNs. This thesis introduces various strategies to tackle these challenges and empower GNNs on real-world tasks.

For the domain-specific challenges, in this thesis, we especially focus on challenges in the chemistry domain, which plays a pivotal role in the drug discovery process. Considering the significant resources needed for labeling through wet lab experiments, the AI for chemistry domain struggles with the scarcity of labeled datasets. To address this, we present a comprehensive set of strategies that span model-based and data-based strategies alongside a hybrid method. These methods ingeniously utilize the diversity of data, models, and molecular representations to compensate for the lack of labels in individual datasets. For the inherent challenges, this thesis introduces strategies to overcome two main challenges: scalability and degree-based issues, especially in the context of link prediction tasks. Both of these two challenges originate from the mechanism of GNNs, which involves the iterative aggregation of neighboring nodes' information to update each central node. For the scalability issue, our work not only preserves GNNs' prediction performance but also significantly boosts inference speed. Regarding degree bias, our work highly improves the effectiveness of GNNs for underrepresented nodes with very light additional computational costs. These contributions not only address critical gaps in applying GNNs to specific domains but also lay the groundwork for future exploration in the broader field of graph-based real-world tasks.

Attributed graphs are constructed from a public dataset \footnote{http://www.robots.ox.ac.uk/~vgg/research/affine/}, which contains eight sets of pictures, covers five common picture transformations: viewpoint changes, scale changes, image blur, JPEG compression, and illumination.

Nodes and corresponding features are extract by SIFT.

@misc{shen2024csgo,
title={CSGO: Constrained-Softassign Gradient Optimization For Large Graph Matching},
author={Binrui Shen and Qiang Niu and Shengxin Zhu},
year={2024},
eprint={2208.08233},
archivePrefix={arXiv},
primaryClass={math.CO},
url={https://arxiv.org/abs/2208.08233},
}

Three temporal graph datasets for node classification under distribution shift.

DBLP-Easy and DBLP-Hard are citation graph datasets. PharmaBio is a collaboration graph dataset.

Vertices are scientific publications, edges are either citations (DBLP) or at-least-one-common-author relationships (PharmaBio).

The task is to classify the vertices of the graph into the respective conference/journal venues (DBLP) or journal categories (PharmaBio). In the DBLP datasets, new classes may appear over time.

Each dataset follows the structure:

• adjlist.txt -- the graph structure encoded as adjacency lists: in each row, the first entry is the source vertex, the remaining entries are adjacent vertices

• X.npy -- numpy serialized format for node features indexed by node id corresponding to adjlist.txt

• y.npy -- numpy serialized format for node labels indexed by node id corresponding to adjlist.txt

• t.npy -- numpy serialized format for time steps indexed by node id corresponding to adjlist.txt

A paper describing our incremental training and evaluation framework is published in IJCNN 2021 (Pre-print on arXiv: https://arxiv.org/abs/2006.14422).

If you use these datasets in your research, please cite the corresponding paper:

@inproceedings{galke2021lifelong, author={Galke, Lukas and Franke, Benedikt and Zielke, Tobias and Scherp, Ansgar}, booktitle={2021 International Joint Conference on Neural Networks (IJCNN)}, title={Lifelong Learning of Graph Neural Networks for Open-World Node Classification}, year={2021}, volume={}, number={}, pages={1-8}, doi={10.1109/IJCNN52387.2021.9533412} }

This repository is part of the Ph.D. thesis of Isabelle M. van Schilt, Delft University of Technology.

This repository is used to generate a graph of open-source sea and airport data. For this, open-source data of the shipping schedules given by MSC, Maersk, HMM, and Evergreen is used. The data is collected from the websites of the shipping companies (see also https://github.com/EwoutH/shipping-data). The data is then processed to generate a graph of the shipping schedules, including the distributions of the shipping schedules. The graph is used to analyze the shipping schedules and to identify the most important ports in the network. Airport data is collected from the open-source OpenFlights database.

As case study, we collect data on CN-HK to main ports in the USA, and mostly MSC data on South America to NL-BE.

This repository is used for developing various graphs on open-source data and automatically running it as a simulation model in the repository: complex_stylized_supply_chain_model_generator

MS-BioGraphs are a family of sequence similarity graph datasets with up to 2.5 trillion edges. The graphs are weighted edges and presented in compressed WebGraph format. The dataset include symmetric and asymmetric graphs. The largest graph has been created by matching sequences in Metaclust dataset with 1.7 billion sequences. These real-world graph dataset are useful for measuring contributions in High-Performance Computing and High-Performance Graph Processing.

Graph drawing, involving the automatic layout of graphs, is vital for clear data visualization and interpretation but poses challenges due to the optimization of a multi-metric objective function, an area where current search-based methods seek improvement. In this paper, we investigate the performance of Jaya algorithm for automatic graph layout with straight lines. Jaya algorithm has not been previously used in the field of graph drawing. Unlike most population-based methods, Jaya algorithm is a parameter-less algorithm in that it requires no algorithm-specific control parameters and only population size and number of iterations need to be specified, which makes it easy for researchers to apply in the field. To improve Jaya algorithm’s performance, we applied Latin Hypercube Sampling to initialize the population of individuals so that they widely cover the search space. We developed a visualization tool that simplifies the integration of search methods, allowing for easy performance testing of algorithms on graphs with weighted aesthetic metrics. We benchmarked the Jaya algorithm and its enhanced version against Hill Climbing and Simulated Annealing, commonly used graph-drawing search algorithms which have a limited number of parameters, to demonstrate Jaya algorithm’s effectiveness in the field. We conducted experiments on synthetic datasets with varying numbers of nodes and edges using the Erdős–Rényi model and real-world graph datasets and evaluated the quality of the generated layouts, and the performance of the methods based on number of function evaluations. We also conducted a scalability experiment on Jaya algorithm to evaluate its ability to handle large-scale graphs. Our results showed that Jaya algorithm significantly outperforms Hill Climbing and Simulated Annealing in terms of the quality of the generated graph layouts and the speed at which the layouts were produced. Using improved population sampling generated better layouts compared to the original Jaya algorithm using the same number of function evaluations. Moreover, Jaya algorithm was able to draw layouts for graphs with 500 nodes in a reasonable time.

Description: this corpus was designed as an experimental benchmark for a task of signed graph classification. It is composed of three datasets derived from external sources and adapted to our needs:

SpaceOrigin Conversations [1]: set of conversational graphs, each one associated to a situation of verbal abuse vs. normal situation. These conversations model interactions happening in chatrooms hosted by an MMORPG/ The graphs were originally unsigned: we attributed signed to the edges based on the polarity of the exchanged messages.

Correlation Clustering Instances [2]: set of graph generated randomly as instances of the Correlation Clustering problem, which consists in partitioning signed graphs. These graphs are not associated in any class in the original paper. We proposed a class based on certain features of the space of optimal solutions explored in [2].

European Parliament Roll-Calls [3]: vote networks extracted from the activity of French Members of the European Parliament. The original data does not have any class associated to the networks: we proposed one based on the number of political factions identified in each network in [3].

These data were used in [4] in order to train and assess various representation learning methods. The authors proposed Signed Graph2vec, a signed variant of Graph2vec; WSGCN, a whole-graph variant of Signed Graph Convolutional Networks (SGCN), and use an aggregated version of Signed Network Embeddings (SiNE) as a baseline. The article provides more information regarding the properties of the datasets, and how they were constituted.

Software: the software used to train the representation learning methods and classifiers is publicly available online: SWGE.

References:

Papegnies, É.; Labatut, V.; Dufour, R. & Linarès, G. Conversational Networks for Automatic Online Moderation. IEEE Transactions on Computational Social Systems, 2019, 6:38-55. DOI: 10.1109/TCSS.2018.2887240 ⟨hal-01999546⟩

Arınık, N.; Figueiredo, R. & Labatut, V. Multiplicity and Diversity: Analyzing the Optimal Solution Space of the Correlation Clustering Problem on Complete Signed Graphs. Journal of Complex Networks, 2020, 8(6):cnaa025. DOI: 10.1093/comnet/cnaa025 ⟨hal-02994011⟩

Arınık, N.; Figueiredo, R. & Labatut, V. Multiple partitioning of multiplex signed networks: Application to European parliament votes. Social Networks, 2020, 60:83-102. DOI: 10.1016/j.socnet.2019.02.001 ⟨hal-02082574⟩

Cécillon, N.; Labatut, V.; Dufour, R. & Arınık, N. Whole-Graph Representation Learning For the Classification of Signed Networks. IEEE Access, 2024, 12:151303-151316. DOI: 10.1109/ACCESS.2024.3472474 ⟨hal-04712854⟩

Funding: part of this work was funded by a grant from the Provence-Alpes-Côte-d'Azur region (PACA, France) and the Nectar de Code company.

Citation: If you use this data or the associated source code, please cite article [4]:

@Article{Cecillon2024, author = {Cécillon, Noé and Labatut, Vincent and Dufour, Richard and Arınık, Nejat}, title = {Whole-Graph Representation Learning For the Classification of Signed Networks}, journal = {IEEE Access}, year = {2024}, volume = {12}, pages = {151303-151316}, doi = {10.1109/ACCESS.2024.3472474},}

As post hoc explanations are increasingly used to understand the behavior of Graph Neural Networks (GNNs), it becomes crucial to evaluate the quality and reliability of GNN explanations. However, assessing the quality of GNN explanations is challenging as existing graph datasets have no or unreliable ground-truth explanations for a given task. Here, we introduce a synthetic graph data generator, ShapeGGen, which can generate a variety of benchmark datasets (e.g., varying graph sizes, degree distributions, homophilic vs. heterophilic graphs) accompanied by ground-truth explanations. Further, the flexibility to generate diverse synthetic datasets and corresponding ground-truth explanations allows us to mimic the data generated by various real-world applications. We include ShapeGGen and additional XAI-ready real-world graph datasets into an open-source graph explainability library, GraphXAI. In addition, GraphXAI provides a broader ecosystem of data loaders, data processing functions, synthetic and real-world graph datasets with ground-truth explanations, visualizers, GNN model implementations, and a set of evaluation metrics to benchmark the performance of any given GNN explainer.

10th DIMACS Implementation Challenge

Updated July 2012

http://www.cc.gatech.edu/dimacs10/index.shtml http://www.cise.ufl.edu/research/sparse/dimacs10

As stated on their main website ( http://dimacs.rutgers.edu/Challenges/ ), the "DIMACS Implementation Challenges address questions of determining realistic algorithm performance where worst case analysis is overly pessimistic and probabilistic models are too unrealistic: experimentation can provide guides to realistic algorithm performance where analysis fails."

For the 10th DIMACS Implementation Challenge, the two related problems of graph partitioning and graph clustering were chosen. Graph partitioning and graph clustering are among the aforementioned questions or problem areas where theoretical and practical results deviate significantly from each other, so that experimental outcomes are of particular interest.

Problem Motivation

Graph partitioning and graph clustering are ubiquitous subtasks in many application areas. Generally speaking, both techniques aim at the identification of vertex subsets with many internal and few external edges. To name only a few, problems addressed by graph partitioning and graph clustering algorithms are:

• What are the communities within an (online) social network?
• How do I speed up a numerical simulation by mapping it efficiently onto a parallel computer?
• How must components be organized on a computer chip such that they can communicate efficiently with each other?
• What are the segments of a digital image?
• Which functions are certain genes (most likely) responsible for?

Challenge Goals

• One goal of this Challenge is to create a reproducible picture of the state-of-the-art in the area of graph partitioning (GP) and graph clustering (GC) algorithms. To this end we are identifying a standard set of benchmark instances and generators.

• Moreover, after initiating a discussion with the community, we would like to establish the most appropriate problem formulations and objective functions for a variety of applications.

• Another goal is to enable current researchers to compare their codes with each other, in hopes of identifying the most effective algorithmic innovations that have been proposed.

• The final goal is to publish proceedings containing results presented at the Challenge workshop, and a book containing the best of the proceedings papers.

Problems Addressed

The precise problem formulations need to be established in the course of the Challenge. The descriptions below serve as a starting point.

• Graph partitioning:

  The most common formulation of the graph partitioning problem for an undirected graph G = (V,E) asks for a division of V into k pairwise disjoint subsets (partitions) such that all partitions are of approximately equal size and the edge-cut, i.e., the total number of edges having their incident nodes in different subdomains, is minimized. The problem is known to be NP-hard.

• Graph clustering:

  Clustering is an important tool for investigating the structural properties of data. Generally speaking, clustering refers to the grouping of objects such that objects in the same cluster are more similar to each other than to objects of different clusters. The similarity measure depends on the underlying application. Clustering graphs usually refers to the identification of vertex subsets (clusters) that have significantly more internal edges (to vertices of the same cluster) than external ones (to vertices of another cluster).

There are 12 data sets in the DIMACS10 collection:

clustering: real-world graphs commonly used as benchmarks coauthor: citation and co-author networks Delaunay: Delaunay triangulations of random points in the plane dyn-frames: frames from a 2D dynamic simulation Kronecker: synthetic graphs from the Graph500 benchmark numerical: graphs from numerical simulation random: random geometric graphs (random points in the unit square) streets: real-world street networks Walshaw: Chris Walshaw's graph partitioning archive matrix: graphs from the UF collection (not added here) redistrict: census networks star-mixtures : artificially generated from sets of real graphs

Some of the graphs already exist in the UF Collection. In some cases, the original graph is unsymmetric, with values, whereas the DIMACS graph is the symmetrized pattern of A+A'. Rather than add duplicate patterns to the UF Collection, a MATLAB script is provided at http://www.cise.ufl.edu/research/sparse/dimacs10 which downloads each matrix from the UF Collection via UFget, and then performs whatever operation is required to convert the matrix to the DIMACS graph problem. Also posted at that page is a MATLAB code (metis_graph) for reading the DIMACS *.graph files into MATLAB.

https://sparse.tamu.edu/DIMACS10

Global Graph Technology market size is expected to reach $14.21 billion by 2029 at 22%, segmented as by software, graph database software, graph analytics software, graph visualization software, graph query language software

Graph Analytics Market size was valued at USD 77.1 Million in 2024 and is projected to reach USD 637.1 Million by 2032, growing at a CAGR of 35.1% during the forecast period 2026 to 2032.

Global Graph Analytics Market Drivers The market drivers for the Graph Analytics Market can be influenced by various factors. These may include:

Growing Need for Data Analysis: In order to extract insightful information from the massive amounts of data generated by social media, IoT devices, and corporate transactions, there is a growing need for sophisticated analytics tools like graph analytics.

Growing Uptake of Big Data Tools: Graph analytics solutions are becoming more and more popular due to the spread of big data platforms and technology. Businesses are using these technologies to improve the efficiency of their analysis of intricately linked datasets.

Developments in AI and ML: The capabilities of graph analytics solutions are being improved by advances in machine learning and artificial intelligence. These technologies make it possible for recommendation systems, anomaly detection, and forecasts based on graph data to be more accurate.

Increasing Recognition of the Advantages of Graph Databases: Businesses are realizing the advantages of graph databases for handling and evaluating highly related data. Consequently, there's been a sharp increase in the use of graph analytics tools to leverage the potential of graph databases for diverse applications.

The use of advanced analytics solutions, such as graph analytics, for fraud detection, cybersecurity, and risk management is becoming more and more important as a result of the increase in cyberthreats and fraudulent activity.

Demand for Personalized suggestions: Companies in a variety of sectors are using graph analytics to provide their clients with suggestions that are tailored specifically to them. Personalized recommendations increase consumer engagement and loyalty on social networking, e-commerce, and entertainment platforms.

Analysis of Networks and Social Media is Necessary: In order to comprehend relationships, influence patterns, and community structures, networks and social media data must be analyzed using graph analytics. The capacity to do this is very helpful for security agencies, sociologists, and marketers.

Government programs and Regulations: The need for graph analytics solutions is being driven by regulations pertaining to data security and privacy as well as government programs aimed at encouraging the adoption of data analytics. These tools are being purchased by organizations in order to guarantee compliance and reduce risks.

Emergence of Industry-specific Use Cases: Graph analytics is finding applications in a number of areas, such as healthcare, finance, retail, and transportation. These use cases include supply chain management, customer attrition prediction, and financial fraud detection in addition to patient care optimization.

Technological Developments in Graph Analytics Tools: As graph analytics tools, algorithms, and platforms continue to evolve, their capabilities and performance are being enhanced. Adoption is being fueled by this technological advancement across a variety of industries and use cases.

In light of the exponential growth in information volume, the significance of graph data has intensified. Graph clustering plays a pivotal role in graph data processing by jointly modeling the graph structure and node attributes. Notably, the practical significance of multi-view graph clustering is heightened due to the presence of diverse relationships within real-world graph data. Nonetheless, prevailing graph clustering techniques, predominantly grounded in deep learning neural networks, face challenges in effectively handling multi-view graph data. These challenges include the incapability to concurrently explore the relationships between multiple view structures and node attributes, as well as difficulties in processing multi-view graph data with varying features. To tackle these issues, this research proposes a straightforward yet effective multi-view graph clustering approach known as SLMGC. This approach uses graph filtering to filter noise, reduces computational complexity by extracting samples based on node importance, enhances clustering representations through graph contrastive regularization, and achieves the final clustering outcomes using a self-training clustering algorithm. Notably, unlike neural network algorithms, this approach avoids the need for intricate parameter settings. Comprehensive experiments validate the supremacy of the SLMGC approach in multi-view graph clustering endeavors when contrasted with prevailing deep neural network techniques.

This vector tile layer presents the World Navigation Map style (World Edition) and provides a basemap for the world, featuring a Navigation style designed for use during the day in mobile devices. This comprehensive street map includes highways, major roads, minor roads, railways, water features, cities, parks, landmarks, building footprints, and administrative boundaries. This vector tile layer provides unique capabilities for customization, high-resolution display, and use in mobile devices.This vector tile layer is built using the same data sources used for other Esri Vector Basemaps. For details on data sources contributed by the GIS community, view the map of Community Maps Basemap Contributors. Esri Vector Basemaps are updated monthly.This layer is used in the Navigation web map included in ArcGIS Living Atlas of the World.See the Vector Basemaps group for other vector tile layers. Customize this StyleLearn more about customizing this vector basemap style using the Vector Tile Style Editor. Additional details are available in ArcGIS Online Blogs and the Esri Vector Basemaps Reference Document.

Abstract (en): Knowledge about the general graph structure of this graph is important for designing ranking methods for search engines. To amend the ranking calculated by search engines for different websites, search engine optimization agencies focus on linkage structure for their clients. An extreme appearance of ranking manipulation manifests in spam networks, where pages and websites publishing dubious content try to increase their ratings by setting a massive number of links to other pages and retrieve backlinks. The WDC Hyperlink Graph aggregated by pay-level-domain has been extracted from the Common Crawl 2012 web corpus and covers 43 million pay-level-domains, linked by 623 million connections which have been derived from hyperlinks between the pages contained in the pay-level-domains.

Graph Neural Networks (GNNs) have gained traction across different domains such as transportation, bio-informatics, language processing, and computer vision. However, there is a noticeable absence of research on applying GNNs to supply chain networks. Supply chain networks are inherently graphlike in structure, making them prime candidates for applying GNN methodologies. This opens up a world of possibilities for optimizing, predicting, and solving even the most complex supply chain problems. A major setback in this approach lies in the absence of real-world benchmark datasets to facilitate the research and resolution of supply chain problem using GNNs. To address the issue, we present a real-world benchmark dataset for temporal tasks, obtained from one of the leading FMCG companies in Bangladesh, focusing on supply chain planning for production purposes. The dataset includes temporal data as node features to enable sales predictions, production planning, and the identification of factory issues. By utilizing this dataset, researchers can employ GNNs to address numerous supply chain problems, thereby advancing the field of supply chain analytics and planning.

Dataset GitHub arXiv PDF on arXiv

Read the paper to learn more details and data statistics.

The Global Graph Database market size is estimated to reach $9.59 billion by 2029 at 24.2%, and is projected to grow demand for personalized marketing is driving the growth of the graph database market.

Global Knowledge Graph market size is expected to reach $3.69 Billion by 2029 at 22.9%, rapid growth in data volume and complexity driving market due to need for efficient data organization and analysis

Graph Database Market size was valued at USD 2.86 Billion in 2024 and is projected to reach USD 14.58 Billion by 2032, growing at a CAGR of 22.6% from 2026 to 2032.

Global Graph Database Market Drivers

The growth and development of the Graph Database Market is attributed to certain main market drivers. These factors have a big impact on how Graph Database are demanded and adopted in different sectors. Several of the major market forces are as follows:

Growth of Connected Data: Graph databases are excellent at expressing and querying relationships as businesses work with datasets that are more complex and interconnected. Graph databases are becoming more and more in demand as connected data gains significance across multiple industries.

Knowledge Graph Emergence: In fields like artificial intelligence, machine learning, and data analytics, knowledge graphs—which arrange information in a graph structure—are becoming more and more popular. Knowledge graphs can only be created and queried via graph databases, which is what is causing their widespread use.

Analytics and Machine Learning Advancements: Graph databases handle relationships and patterns in data effectively, enabling applications related to advanced analytics and machine learning. Graph databases are becoming more and more in demand when combined with analytics and machine learning as businesses want to extract more insights from their data.

Real-Time Data Processing: Graph databases can process data in real-time, which makes them appropriate for applications that need quick answers and insights. In situations like fraud detection, recommendation systems, and network analysis, this is especially helpful.

Increasing Need for Security and Fraud Detection: Graph databases are useful for fraud security and detection applications because they can identify patterns and abnormalities in linked data. The growing need for graph databases in security solutions is a result of the ongoing evolution of cybersecurity threats.

As of 2024, the estimated number of internet users worldwide was 5.5 billion, up from 5.3 billion in the previous year. This share represents 68 percent of the global population. Internet access around the world Easier access to computers, the modernization of countries worldwide, and increased utilization of smartphones have allowed people to use the internet more frequently and conveniently. However, internet penetration often pertains to the current state of development regarding communications networks. As of January 2023, there were approximately 1.05 billion total internet users in China and 692 million total internet users in the United States. Online activities Social networking is one of the most popular online activities worldwide, and Facebook is the most popular online network based on active usage. As of the fourth quarter of 2023, there were over 3.07 billion monthly active Facebook users, accounting for well more than half of the internet users worldwide. Connecting with family and friends, expressing opinions, entertainment, and online shopping are amongst the most popular reasons for internet usage.