Explore the evolution of Machine Learning in Graphs, from traditional ML tasks to advanced Graph Neural Networks (GNNs). Discover key concepts like feature engineering, tools like PyG, and types of ML tasks in graphs. Uncover insights into node-level, graph-level, and community-level predictions, an

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This paper introduces the Localised Adaptive Spatial-Temporal Graph Neural Network model, focusing on the importance of spatial-temporal data modeling in graph structures. The challenges of balancing spatial and temporal dependencies for accurate inference are addressed, along with the use of distri

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Graph Neural Networks (GNNs) are a versatile form of neural networks that encompass various network architectures like NNs, CNNs, and RNNs, as well as unsupervised learning models such as RBM and DBNs. They find applications in diverse fields such as object detection, machine translation, and drug d

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This comprehensive presentation delves into the fundamentals of Neo4j graph database, covering topics such as the definition of graph databases, reasons for their usage, insights into Neo4j and Cypher, practical applications like data flow analysis, and hands-on instructions on creating and querying

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Development of mathematical theories such as model theory, proof theory, set theory, recursion theory, and computational complexity is discussed, starting from historical perspectives with Dedekind and Peano to Godel's theorems, recursion theory's golden age in the 1930s, and advancements in proof t

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Graph-based data science offers a powerful approach to analyzing data by leveraging graph structures. This involves using graph representation, analysis algorithms, ML/AI techniques, kernels, embeddings, and neural networks. Real-world examples show the utility of data graphs in various domains like

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The theory of firms is explored through the Neoclassical and Modern perspectives. Neoclassical theory focuses on profit maximization, while Modern theory delves into managerial, principal-agent, and transaction cost theories. The discussion covers criticisms of Neoclassical theory and the essential

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Explore the intriguing concepts of the Friendship Theorem and Freshman's Dream in graph theory along with examples and visual illustrations. Learn about common friends, relationships between vertices and edges, and what defines a graph in a concise yet comprehensive manner.

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Graph Theory Matchings have a rich history dating back to the 9th century AD. Distinct Representatives and Hall's Theorem play important roles in determining matchings in graphs. Understanding concepts like bipartite graphs, maximum matchings, and Hall's Marriage Theorem is essential in graph theory

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Delve into the realm of Deep Graph Theory where graph theory statements are analyzed beyond their conventional scope to uncover philosophical insights and correct misunderstandings. Discover the essence of trees, forests, and the unique relationship where every tree is regarded as a forest. Addition

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At the turn of the century, the discovery of the photoelectric effect challenged the wave theory of light, leading to the development of the quantum theory by Max Planck and Albert Einstein. This new theory introduced the concept of discrete energy units known as quanta, bridging the gap between wav

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Delve into the basics of graph theory with topics like graph embeddings, graph plotting, Kuratowski's theorem, planar graphs, Euler characteristic, trees, and more. Explore the principles behind graphs, their properties, and key theorems that define their structure and connectivity.

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Dive into the world of association rules with graph patterns, where relationships and connections are analyzed through nodes and edges. Discover how to define association rules, identify customers, and uncover interesting patterns using graph-based techniques. Explore traditional and graph-pattern a

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An intriguing mathematical problem is presented where new faculty members at TIMS must be assigned to coffee lounge alcoves in a way that ensures no two new members meet after the first day. By constructing a graph based on meet-up timings, analyzing clashes, and determining intervals, this scenario

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In this study by Uriel Feige and Roee David from the Weizmann Institute, the effect of randomness on planted 3-coloring models is investigated. The research delves into the NP-hard nature of 3-coloring problems, introducing a hosted coloring framework that involves choices like the host graph and th

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This research discusses the challenges in managing large graphs on multi-core systems and introduces Grace, an in-memory graph management and processing system with optimizations for graph-specific and multi-core-specific operations. The system keeps the entire graph in memory in smaller parts and p

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Delve into the fascinating world of graph colorings, chromatic polynomials, and notable conjectures in discrete geometry. Explore the impact of June Huh in bringing Hodge theory to combinatorics and his proof of various mathematical conjectures. Uncover the significance of the four-color theorem, co

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Maria's bike journey graph depicts her distance from home as she rode to meet friends and run errands before returning home. The graph shows her stops for errands, changes in direction, and her path back home. By interpreting the key features of the graph, such as intercepts and intervals, we can an

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The content discusses the concept of maximal independent sets in graph theory. It defines independent, maximal, and maximum sets, highlighting the difficulty in finding a maximum independent set due to its NP-hard nature. Sequential and parallel algorithms for finding maximal independent sets are pr

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Delve into the world of discrete mathematics with a focus on graph theory. Learn about graphs, their properties, and essential theorems. Discover how graphs model relations in various applications like network routing, GPS guidance, and chemical reaction simulations. Explore graph terminology, theor

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Balanced graph edge partitioning is a crucial problem in graph computation, machine learning, and graph databases. It involves partitioning a graph's vertices or edges into balanced components while minimizing cut costs. This process is essential for various real-world applications such as iterative

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Explore the concepts of cliques and independent sets in graph theory through C++ programming with Cynthia Bailey Lee's Creative Commons licensed materials. Understand NP-complete graph problems and learn about coding implementations for determining cliques and independent sets efficiently.

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Dive into the concept of minimal spanning trees in graph theory with a focus on algorithms like Prim's and Kruskal's. Explore the definition of trees, spanning trees, and weighted graphs. Learn about the importance of finding the minimal spanning tree in a graph and how it contributes to optimizatio

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Explore the concept of spanning trees and minimum spanning trees in graph theory through an in-depth lecture outline covering topics like Cut Property, Cycle Property, Kruskal's Algorithm, and more. Delve into the significance of Minimum Spanning Trees (MSTs) as the lowest-cost spanning tree of a gr

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Graph pattern matching in social networks presents challenges such as costly queries, excessive results, and query focus issues. The complexity of top-k and diversified pattern matching problems requires heuristic algorithms for efficient solutions. Finding best candidates for project roles involves

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Explore various theories of interest in economics, including the Classical Theory, Liquidity Preference Theory by Keynes, Productivity Theory, Abstinence Theory, Time-Preference Theory, Fisher's Time Preference Theory, and the Loanable Fund Theory. These theories offer different perspectives on the

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In this detailed piece, Subhash Khot, Dor Minzer, Dana Moshkovitz, and Muli Safra explore the fascinating concept of Small Set Expansion in Johnson Graphs. The Johnson Graph is defined as a representation where nodes are sets of size K in a universe of size N, and two sets are connected if they inte

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Seastar presents a vertex-centric programming approach for Graph Neural Networks, showcasing better performance in graph analytic tasks compared to traditional methods. The research introduces the SEAStar computation pattern and discusses GNN programming abstractions, execution, and limitations. Dee

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Explore testable bounded degree graph properties, sparse graphs, d-bounded degree graphs, hyperfinite graphs, arboricity, maximum matching algorithms, and sublinear time approximation algorithms in graph data streams. Learn about various graph models and properties with examples, showcasing the impo

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Explore the world of graph modeling and DFS applications through lectures on graph vocabulary, edge classification in directed graphs, and the use of DFS to find cycles. Discover the significance of tree edges, back edges, forward edges, and cross edges in graph traversal. Learn how DFS can be utili

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This content delves into graph-based knowledge representation in modelling, detailing concepts such as recipe-ingredient relationships, formalisms for generalizing graph representation, and conceptual graphs by John F. Sowa. It explores how different interpretations describe the association between

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Graph databases offer a flexible way to manage data by representing relationships between nodes. Neo4j is a popular graph database system that uses Cypher for querying. This guide provides insights into graph database concepts, advantages, and getting started with Neo4j, including creating nodes and

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Presented by Manvitha Nellore, this content addresses real-world train track problems in busy cities by proposing solutions through interval graphs and graph theory. The approach involves allotting tracks to trains by scheduling with time intervals to avoid conflicts. An interval graph is defined, a

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Adjacency labeling schemes involve assigning L-bit labels to vertices in a graph for efficient edge determination. The concept of induced-universal graphs is explored, where a graph is universal for a family F if all graphs in F are subgraphs of it. Theorems and lower bounds related to adjacency lab

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Dive into the challenge of assigning tropical fish into tanks efficiently based on predator-prey relationships, water conditions, and compatibility. Explore the graph theory approach to determine the minimum number of tanks needed, construct a graph representing fish compatibility, identify the prob

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Explore the basics of graph theory including graph properties, theorems, bipartite graphs, matchings, vertices, and degrees. Learn about partitioning, Hall's theorem, and how graphs can be used to represent relationships.

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This content delves into the preprocessing, computing, post-processing, and analysis of raw XML data for graph-based algorithms. It covers topics such as data ETL, graph analytics, PageRank computation, and identifying top users. Various tools and frameworks like GraphX, Spark, Giraph, and GraphLab

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Exploring the concept of minimum spanning trees in undirected, weighted graphs. A spanning tree is a connected acyclic subgraph that includes all vertices of the original graph. The Minimum Spanning Tree (MST) problem involves finding the tree with the smallest total edge weight. The cycle property

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Graph data structure is a fundamental tool in computer science, comprising nodes (vertices) connected by edges to represent relationships. This comprehensive guide covers various aspects of graphs, such as definitions, types (undirected, directed, weighted), terminology (adjacent nodes, paths, degre

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Graph algorithms play a crucial role in solving problems represented as networks, maps, paths, plans, and resource flow. This content delves into ways to find connectivity in graphs and algorithms for determining shortest paths. It discusses graph representations using adjacency matrices and lists,

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