منابع مشابه
Eigenvalues, Expanders and Superconcentrators
Explicit construction of families of linear expanders and superconcentrators is relevant to theoretical computer science in several ways. There is essentially only one known explicit construction. Here we show a correspondence between the eigenvalues of the adjacency matrix of a graph and its expansion properties, and combine it with results on Group Representations to obtain many new examples ...
متن کاملExpanders and Eigenvalues
We denote by G = (V,E) a d-regular graph on n = |V | nodes with no multiple edges and no self-loops. We denote by A its adjacency matrix. Thus, A is a symmetric n×n-matrix in which each element either is zero or one and each row and column contains exactly d ones and n− d zeros. We denote by d = μ1 ≥ . . . ≥ μn the eigenvalues of A, and we denote by d = λ1 ≥ . . . ≥ λn the corresponding absolut...
متن کاملEigenvalues and Expanders
Linear expanders have numerous applications to theoretical computer science. Here we show that a regular bipartite graph is an expander ifandonly if the second largest eigenvalue of its adjacency matrix is well separated from the first. This result, which has an analytic analogue for Riemannian manifolds enables one to generate expanders randomly and check efficiently their expanding properties...
متن کاملLecture 2: Eigenvalues and Expanders 2.1 Lecture Outline
There is a connection between the expansion of a graph and the eigengap (or spectral gap) of the normalized adjacency matrix (that is, the gap between the first and second largest eigenvalues). Recall that the largest eigenvalue of the normalized adjacency matrix is 1; denote it by λ1 and denote the second largest eigenvalue by λ2. We will see that a large gap (that is, small λ2) implies good e...
متن کاملEigenvalues, geometric expanders, sorting in rounds, and Ramsey theory
Expanding graphs are relevant to theoretical computer science in several ways. Here we show that the points versus hyperplanes incidence graphs of finite geometries form highly (nonlinear) expanding graphs with essentially the smallest possible number of edges. The expansion properties of the graphs are proved using the eigenvalues of their adjacency matrices. These graphs enable us to improve ...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 1986
ISSN: 0209-9683,1439-6912
DOI: 10.1007/bf02579166