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The signless Laplacian matrix of hypergraphs [PDF]
In this article, we define signless Laplacian matrix of a hypergraph and obtain structural properties from its eigenvalues. We generalize several known results for graphs, relating the spectrum of this matrix to structural parameters of the hypergraph ...
Cardoso Kauê, Trevisan Vilmar
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On Eigenvalues of Laplacian Matrix for a Class of Directed Signed Graphs [PDF]
The eigenvalues of the Laplacian matrix for a class of directed graphs with both positive and negative weights are studied. First, a class of directed signed graphs is investigated in which one pair of nodes (either connected or not) is perturbed with ...
Ahmadizadeh, Saeed+3 more
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On the Spectrum of Laplacian Matrix [PDF]
Let G be a simple graph of order n . The matrix ℒ
Akbar Jahanbani+2 more
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Bipartite subgraphs and the signless Laplacian matrix
For a connected graph G, we derive tight inequalities relating the smallest signless Laplacian eigenvalue to the largest normalized Laplacian eigenvalue. We investigate how vectors yielding small values of the Rayleigh quotient for the signless Laplacian matrix can be used to identify bipartite subgraphs.
Steve Kirkland, Debdas Paul
semanticscholar +5 more sources
Forest matrices around the Laplacian matrix [PDF]
We study the matrices Q_k of in-forests of a weighted digraph G and their connections with the Laplacian matrix L of G. The (i,j) entry of Q_k is the total weight of spanning converging forests (in-forests) with k arcs such that i belongs to a tree ...
Agaev+61 more
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Trees with matrix weights: Laplacian matrix and characteristic-like vertices [PDF]
It is known that there is an alternative characterization of characteristic vertices for trees with positive weights on their edges via Perron values and Perron branches. Moreover, the algebraic connectivity of a tree with positive edge weights can be expressed in terms of Perron value.
Swetha Ganesh, Sumit Mohanty
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Laplacian Matrix for Dimensionality Reduction and Clustering [PDF]
Many problems in machine learning can be expressed by means of a graph with nodes representing training samples and edges representing the relationship between samples in terms of similarity, temporal proximity, or label information. Graphs can in turn be represented by matrices. A special example is the Laplacian matrix, which allows us to assign each
Laurenz Wiskott, Fabian Schönfeld
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On the spread of the distance signless Laplacian matrix of a graph [PDF]
Let G be a connected graph with n vertices, m edges. The distance signless Laplacian matrix DQ(G) is defined as DQ(G) = Diag(Tr(G)) + D(G), where Diag(Tr(G)) is the diagonal matrix of vertex transmissions and D(G) is the distance matrix of G.
Pirzada S., Haq Mohd Abrar Ul
doaj +2 more sources
Random matrix analysis of network Laplacians [PDF]
We analyze eigenvalues fluctuations of the Laplacian of various networks under the random matrix theory framework. Analyses of random networks, scale-free networks and small-world networks show that nearest neighbor spacing distribution of the Laplacian ...
Albert+39 more
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Synchronization under matrix-weighted Laplacian [PDF]
Synchronization in a group of linear time-invariant systems is studied where the coupling between each pair of systems is characterized by a different output matrix.
Tuna, S. Emre
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