Graph expander
WebMar 1, 2024 · Abstract. Expander graphs are highly connected graphs that have numerous applications in statistical physics, pure mathematics and in computer science. The … WebExpander graphs are universally useful in computer science and have many applications in de-randomization, circuit complexity, error correcting codes, communication and sorting …
Graph expander
Did you know?
WebDec 1, 2024 · Finally, we propose a definition of a matrix-weighted expander graph and discuss its implications. 2. Matrix-weighted graphs 2.1. Definitions We will view a weighted graph as a structure built on top of an underlying unweighted, undirected graph. Let G be a graph with vertex set V and edge set E. In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander constructions have spawned research in pure and applied mathematics, with several applications to complexity theory, design of robust computer … See more Intuitively, an expander graph is a finite, undirected multigraph in which every subset of the vertices that is not "too large" has a "large" boundary. Different formalisations of these notions give rise to different notions of … See more The original motivation for expanders is to build economical robust networks (phone or computer): an expander with bounded degree is precisely … See more • Algebraic connectivity • Zig-zag product • Superstrong approximation • Spectral graph theory See more The expansion parameters defined above are related to each other. In particular, for any d-regular graph G, Consequently, for … See more There are three general strategies for explicitly constructing families of expander graphs. The first strategy is algebraic and group-theoretic, the second strategy is analytic and uses See more 1. ^ Hoory, Linial & Wigderson (2006) 2. ^ Definition 2.1 in Hoory, Linial & Wigderson (2006) 3. ^ Bobkov, Houdré & Tetali (2000) See more • Brief introduction in Notices of the American Mathematical Society • Introductory paper by Michael Nielsen • Lecture notes from a course on expanders (by Nati Linial and Avi Wigderson) See more
WebOct 6, 2024 · Expander Graph Propagation. Deploying graph neural networks (GNNs) on whole-graph classification or regression tasks is known to be challenging: it often … WebIn the mathematical field of spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory).Such …
WebI need to construct d-regular expander graph for some small fixed d (like 3 or 4) of n vertices. What is the easiest method to do this in practice? Constructing a random d … WebNov 5, 2008 · Expander graphs based on GRH with an application to elliptic curve cryptography. We present a construction of expander graphs obtained from Cayley …
WebLet d 5. A random d-regular graph is a 1=2-expander graph with high probability. 1. Theorem 4. For all d 5, for all nsu ciently large there exists a strongly explicit d-regular 1=2-expander graph. Let’s be explicit about what \explicit" means. De nition 5. A graph is explicit if given nin time poly(n) we can compute an adjacency matrix
WebMar 6, 2024 · A disconnected graph is not an expander, since the boundary of a connected component is empty. Every connected graph is an expander; however, different … candyland cupcakesWebAbstract Expander graphs are highly connected and sparse graphs that have a lot of applicationsinnetworksandcomputers. Thispropertyoveragraphisequalto another ... candyland cutoutsWebExpander graphs are widely used in Theoretical Computer Science, in areas ranging from parallel computation ] to complexity theory and cryptography.z Given an undirected k … candy land darwinWebExpanders and Spectral Methods" o ered at o ered at U.C. Berkeley in Spring 2016. This material is based upon work supported by the National Science Foundation under Grants … fish volleyball gameWebOct 28, 2015: A simple construction of expander graphs. Nov 2, 2015: Sparsification by effective resistance random sampling. Nov 4, 2015: Linear sized sparsifiers. Nov 9, 2015: Fast Laplacian solvers by sparsification. Nov 11, 2015: The spectral gap of planar graphs. (PS 4 due, PS 5 out) Nov 16, 2015: Partitioning in block models. fish vr songWebPeople – Department of Mathematics ETH Zurich fish vocalizationWebApr 14, 2024 · Output of a pseudorandom number generator created using the zig-zag product of a (20,16) and a (16,4) graph. Plot displays the frequency of each number being... fish volunteer transportation