Subgraphs - PowerPoint PPT Presentation

Explore the perception of small subgraphs through the study of graph motifs and experimental design, touching on Gestalt principles of similarity and levels of perceptual processing. The research delves into how distinct objects can be grouped together based on similarity, influencing pattern recogn

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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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Efficiently listing triangles in dynamic graphs is essential for identifying dense subgraphs in social networks. This study focuses on fast triangle listing in large graphs, particularly after batch updates, to find new and deleted triangles. The problem statement involves listing all triangles from

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Discovering top-K interesting subgraphs in information networks is crucial for various applications like network bottlenecks, team selection, resource allocation, and more. This research focuses on developing low-cost indexes and novel algorithms to efficiently detect these subgraphs. The contributi

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Explore the essential concepts of Topological Sorting in Spark GraphX, including necessary background knowledge, stand-alone versus distributed implementations, and practical examples. Delve into Spark GraphX's capabilities, such as RDD manipulation, high-level tools, and graph parallel computation.

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The research explores neighbourhood sampling for local properties on graph streams, focusing on counting subgraphs within 1-neighbourhood of a vertex. It addresses the Triangle Counting Problem and explains the significance of counting triangles in various contexts such as social network analysis an

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Bitruss decomposition is a powerful concept in graph theory to identify cohesive subgraphs in bipartite graphs. This paper by Kai Wang, Xuemin Lin, Lu Qin, Wenjie Zhang, and Ying Zhang presents an efficient approach for computing bitruss numbers of edges in large-scale bipartite graphs. The study ex

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In this overview, we delve into various aspects of frequent subgraph mining, discussing types of graphs, analyzing graphs for data mining tasks, input-output processes, and the goal of discovering repeated subgraphs in graph databases.

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Explore the basics of graph theory, including directed and undirected graphs, graph definitions, terminology, constraints in scheduling, the handshake theorem, and subgraphs. Learn about paths, cycles, acyclic and complete graphs, connectivity, and more. Discover how graphs are used to represent rel

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Planar graphs are characterized by their unique embedding properties, as illustrated by examples like Kuratowski subgraphs. Kuratowski's Theorem from 1930 provides an essential criterion for determining the planarity of a graph based on the absence of certain subgraphs.

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Explore the concept of cut sparsifiers in graph structures, focusing on partitioning graph vertices, minimum-cut values, and algorithms for computing sparse weighted subgraphs. Learn about uniform and non-uniform sampling techniques, concentration arguments, and key lemmas in the field. Discover how

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The Subgraph Testing Model by Oded Goldreich & Dana Ron, focusing on property testing & its application in query complexity. Discover the standard error definitions & the new model testing properties of subgraphs, along with initial observations and comparisons with the bounded-degree graph model.

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Explore the fundamental concepts of graphs, including vertices, edges, directed and simple graphs, complete graphs, subgraphs, Euler circuits, and more. Dive into matrix representations, planar graphs, and graph isomorphism for a comprehensive overview.

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Explore extremal graph theory concepts such as Mantel's and Turan's theorems, complete multipartite graphs, and proof techniques. Understand key results like maximum edge configurations in graphs without certain subgraphs.

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Explore Ramsey Theory, discussing Ramsey's Numbers such as R(2,2), R(3,3), known value ranges, and Ramsey's Theorem proof. Learn about complete graphs, subgraphs, cliques, alphabets, words, and the generalization of Ramsey's Theorem.

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Explore the world of additive spanners in graph structures with state-of-the-art techniques, hitting sets, and subgraphs representing various edge properties. Delve into the recurrent patterns in algorithm design and discover deterministic and randomized algorithms for finding small hitting sets eff

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Explore the Color-Coding method by Alon, Yuster, Zwick, and Patel for finding simple paths, cycles, and subgraphs of specified lengths in graphs efficiently. Learn about random coloring, colorful paths, lemma, and examples in this algorithmic technique.

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Explore the output-sensitive enumeration framework for analyzing cliques, maximal cliques, and dense subgraphs. Utilizing reverse search algorithms and family tree realization techniques to efficiently identify solutions. Discover the complexities and alternative output strategies for optimal comput

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