Results 21 to 30 of about 121,870 (266)
Random matrix analysis of network Laplacians [PDF]
Physica A: Statistical Mechanics and its Applications, 2008 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 of these networks follow Gaussian orthogonal ensemble statistics of random matrix theory ...
Jalan, S., Bandyopadhyay, J.
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Sparse Graph Learning Under Laplacian-Related Constraints
IEEE Access, 2021 We consider the problem of learning a sparse undirected graph underlying a given set of multivariate data. We focus on graph Laplacian-related constraints on the sparse precision matrix that encodes conditional dependence between the random variables ...
Jitendra K. Tugnait
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The normalized distance Laplacian
Special Matrices, 2021 The distance matrix đ(G) of a connected graph G is the matrix containing the pairwise distances between vertices. The transmission of a vertex vi in G is the sum of the distances from vi to all other vertices and T(G) is the diagonal matrix of ...
Reinhart Carolyn
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Incremental eigenpair computation for graph Laplacian matrices: theory and applications [PDF]
, 2017 The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used for spectral clustering and community detection. However, in real-life applications, the number of clusters or communities (say,
Al Hasan, Mohammad +2 more
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Spectral properties of edge Laplacian matrix
, 2023 Let $N(X)$ be the Laplacian matrix of a directed graph obtained from the edge adjacency matrix of a graph $X.$ In this work, we study the bipartiteness property of the graph with the help of $N(X).$ We computed the spectrum of the edge Laplacian matrix for the regular graphs, the complete bipartite graphs, and the trees.
Chauhan, Shivani +1 more
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More on Spectral Analysis of Signed Networks
Complexity, 2018 Spectral graph theory plays a key role in analyzing the structure of social (signed) networks. In this paper we continue to study some properties of (normalized) Laplacian matrix of signed networks. Sufficient and necessary conditions for the singularity
Guihai Yu, Hui Qu
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Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic
Trends in Computational and Applied Mathematics, 2021 We present a linear-time algorithm that computes in a given real interval the number of eigenvalues of any symmetric matrix whose underlying graph is unicyclic.
R. O. Braga +2 more
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Simplicial matrix-tree theorems [PDF]
, 2008 We generalize the definition and enumeration of spanning trees from the setting of graphs to that of arbitrary-dimensional simplicial complexes $\Delta$, extending an idea due to G. Kalai.
Duval, Art M. +2 more
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Estimating mixed-memberships using the symmetric laplacian inverse matrix
Journal of the Korean Statistical Society, 2022 Mixed membership community detection is a challenging problem. In this paper, to detect mixed memberships, we propose a new method Mixed-SLIM which is a spectral clustering method on the symmetrized Laplacian inverse matrix under the degree-corrected mixed membership model.
Huan Qing, Jingli Wang
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International Journal of Robust and Nonlinear Control, EarlyView., 2023 Abstract We propose a hierarchical energy management scheme for aggregating Distributed Energy Resources (DERs) for grid flexibility services. To prevent a direct participation of numerous prosumers in the wholesale electricity market, aggregators, as selfâinterest agents in our scheme, incentivize prosumers to provide flexibility. We firstly model the
Xiupeng Chen +3 more
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