Results 31 to 40 of about 2,858,268 (305)

On the Maximal-Adjacency-Spectrum Unicyclic Graphs with Given Maximum Degree

Mathematical Problems in Engineering, 2020
In this paper, we study the properties and structure of the maximal-adjacency-spectrum unicyclic graphs with given maximum degree. We obtain some necessary conditions on the maximal-adjacency-spectrum unicyclic graphs in the set of unicyclic graphs with n vertices and maximum degree Δ and describe the structure of the maximal-adjacency-spectrum ...
Haizhou Song, Lulu Tian
openaire   +2 more sources

Generating directed networks with prescribed Laplacian spectra [PDF]

, 2020
Complex real-world phenomena are often modeled as dynamical systems on networks. In many cases of interest, the spectrum of the underlying graph Laplacian sets the system stability and ultimately shapes the matter or information flow.
Battistelli, Giorgio, Carletti, Timoteo, Chisci, Luigi, Fanelli, Duccio, Nicoletti, Sara   +4 more
core   +3 more sources

Spectral Theory of Sparse Non-Hermitian Random Matrices [PDF]

, 2019
Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics.
Abou-Chacra R, Aurell E, Barabási A-L, Bickson D, Bordenave C, Brown L G, Castellani T, Coolen A, Cugliandolo L F, Derrida B, Dorogovtsev S N, Efetov K, Erdos P, Erdos P, Fernando Lucas Metz, Fyodorov Y V, Gudowska-Nowak E, Haagerup U, Izaak Neri, Kabashima Y, Kabashima Y, Kühn R, Kühn R, Langville A N, Marrec L, Mehta M L, Neri I, Peron T K D, Reed M, Rogers T, Rogers T, Rogers T, Saade A, Semerjian G, Tim Rogers, Trefethen L N, Weiss Y, Wilkinson J H, Zabrodin A   +38 more
core   +3 more sources

Outliers in spectrum of sparse Wigner matrices [PDF]

Random Struct. Algorithms, 2019
In this paper, we study the effect of sparsity on the appearance of outliers in the semi‐circular law. Let (Wn)n=1∞ be a sequence of random symmetric matrices such that each Wn is n × n with i.i.d.
K. Tikhomirov, Pierre Youssef
semanticscholar   +1 more source

The Laplacian spectral excess theorem for distance-regular graphs [PDF]

, 2014
The spectral excess theorem states that, in a regular graph G, the average excess, which is the mean of the numbers of vertices at maximum distance from a vertex, is bounded above by the spectral excess (a number that is computed by using the adjacency ...
Fiol, Miquel Angel, van Dam, Edwin R.
core   +4 more sources

Hermitian-adjacency matrices and Hermitian energies of mixed graphs

Linear Algebra and Its Applications, 2015
Jianxi Liu, Xueliang Li
semanticscholar   +3 more sources

On the N-spectrum of oriented graphs

Open Mathematics, 2020
Given any digraph D, its non-negative spectrum (or N-spectrum, shortly) consists of the eigenvalues of the matrix AA T, where A is the adjacency matrix of D.
Abudayah Mohammad, Alomari Omar, Sander Torsten   +2 more
doaj   +1 more source

Cycles of length three and four in tournaments [PDF]

, 2019
Linial and Morgenstern conjectured that, among all $n$-vertex tournaments with $d\binom{n}{3}$ cycles of length three, the number of cycles of length four is asymptotically minimized by a random blow-up of a transitive tournament with all but one part of
Chan, Timothy F. N., Grzesik, Andrzej, Kral, Daniel, Noel, Jonathan A.   +3 more
core   +2 more sources

Approximating the Spectrum of a Graph [PDF]

Knowledge Discovery and Data Mining, 2017
The spectrum of a network or graph $G=(V,E)$ with adjacency matrix A , consists of the eigenvalues of the normalized Laplacian $L= I - D^-1/2 A D^-1/2 $.
D. Cohen-Steiner, Weihao Kong, C. Sohler, G. Valiant   +3 more
semanticscholar   +1 more source

Spectral properties of the hierarchical product of graphs [PDF]

, 2016
The hierarchical product of two graphs represents a natural way to build a larger graph out of two smaller graphs with less regular and therefore more heterogeneous structure than the Cartesian product.
Skardal, Per Sebastian, Wash, Kirsti
core   +3 more sources