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 … 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
Expansion in matrix-weighted graphs - ScienceDirect
WebEvery connected graph is an expander; however, different connected graphs have different expansion parameters. The complete graph has the best expansion property, … Webin nite d-regular tree (this is the ultimate expander graph) has its spectral radius equal to 2 p d 1. Proof. The main idea is to study the eigenvalues through the trace of a high even … knoch football hudl
15.1 Cheeger’s Inequality (continued) - University of Washington
WebApr 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... WebExpander codes are linear codes whose factor graphs are bipartite expander graphs. Let us denote the code corresponding to an expander graph Gby C(G). We now establish a useful property of bipartite expander graphs with expansion close to degree D. Lemma 3 Let Gbe a (n;m;D;;D(1 )) expander graph with <1=2. For any S L G such that jSj WebExpander graphs are sparse highly connected graphs with large 2nd eigenvalues, i.e., 2 (1). So, the can be seen as a sparse complete graphs which have 2 = 1. It turns out that … knoch craft show