Forest matrices around the Laplacian matrix

DOI10.1016/S0024-3795(02)00388-9zbMath1017.05073arXivmath/0508178OpenAlexW3099358910MaRDI QIDQ1855402

R. P. Agaev, Pavel Yu. Chebotarev

Publication date: 5 February 2003

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0508178

zbMATH Keywords

matrix-tree theoremweighted digraph

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (37)

Models of latent consensus ⋮ The projection method for continuous-time consensus seeking ⋮ The Grassmann-Berezin calculus and theorems of the matrix-tree type ⋮ State synchronization of multi-agent systems via static or adaptive nonlinear dynamic protocols ⋮ On coefficients of the characteristic polynomial of the Laplace matrix of a weighted digraph and the all minors theorem ⋮ Loop-erased partitioning of a graph: mean-field analysis ⋮ The projection method for reaching consensus and the regularized power limit of a stochastic matrix ⋮ On the characteristic polynomial and eigenvectors in terms of the tree-like structure of a digraph ⋮ Further results on digraphs with completely real Laplacian spectra ⋮ Hitting time quasi-metric and its forest representation ⋮ A generalized inverse for graphs with absorption ⋮ Forest formulas of discrete Green's functions ⋮ On resistance distance of Markov chain and its sum rules ⋮ Drazin-inverse and heat capacity for driven random walkers on the ring ⋮ A new distributed protocol for consensus of discrete-time systems ⋮ A class of graph-geodetic distances generalizing the shortest-path and the resistance distances ⋮ Squared-down passivity-based \(H_\infty\) and \(H_2\) almost synchronization of homogeneous continuous-time multi-agent systems with partial-state coupling via static protocol ⋮ Cyclic coverings of graphs. Counting rooted spanning forests and trees, Kirchhoff index, and Jacobians ⋮ The walk distances in graphs ⋮ Structure of minimum-weight directed forests: related forests and convexity inequalities ⋮ Laplacian dynamics on general graphs ⋮ A combinatorial expression for the group inverse of symmetric \(M\)-matrices ⋮ Spanning forests and the golden ratio ⋮ Laplace spectra of orgraphs and their applications ⋮ A cyclic representation of discrete coordination procedures ⋮ Centrality measure in graphs ⋮ On the spectra of nonsymmetric Laplacian matrices ⋮ Which digraphs with ring structure are essentially cyclic? ⋮ The graph bottleneck identity ⋮ Consensus in asynchronous multiagent systems. I: Asynchronous consensus models ⋮ A first hitting time approach to finding effective spreaders in a network ⋮ Coordination in multiagent systems and Laplacian spectra of digraphs ⋮ Diffusion and consensus on weakly connected directed graphs ⋮ Unnamed Item ⋮ Trees and forests for nonequilibrium purposes: an introduction to graphical representations ⋮ A graph interpretation of the least squares ranking method ⋮ On efficient randomized algorithms for finding the PageRank vector

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On group inverses of \(M\)-matrices with uniform diagonal entries
• A modified Leverrier-Faddeev algorithm for matrices with multiple eigenvalues
• Resolvent expansions of matrices and applications
• An enumerating function for spanning forests with color restrictions
• Matrix tree theorems
• Singular M-matrices and inverse positivity
• The matrix-forest theorem and measuring relations in small social groups
• Tree and forest weights and their application to nonuniform random graphs
• A generalization of the all minors matrix tree theorem to semirings
• Some determinant expansions and the matrix-tree theorem
• Parallel concepts in graph theory
• Graph-theoretic interpretation of the generalized row sum method
• A certain polynomial of a graph and graphs with an extremal number of trees
• Power bounded and exponentially bounded matrices.
• Spanning forests of a digraph and their applications
• Representation and approximation for the Drazin inverse \(A^{(\text{d})}\)
• The matrix of maximum out forests of a digraph and its applications
• On proximity measures for graph vertices
• A combinatorial Laplacian with vertex weights
• Representation and approximation of the outer inverse \(A_{T,S}^{(2)}\) of a matrix \(A\)
• Determinants of Laplacians on graphs
• The number of trees in a graph. I. II
• Block diagonalization
• On $W$-bases of directed graphs
• Matrices, Digraphs, and Determinants
• Generalized matrix tree theorem for mixed graphs
• Expansions of Sums of Matrix Powers
• A Combinatorial Proof of the All Minors Matrix Tree Theorem
• Countingk-component forests of a graph
• The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains
• More on the Souriau–Frame Algorithm and the Drazin Inverse
• A Representation of the Drazin Inverse and Characterizations of the Index
• How to Get a Perfectly Random Sample from a Generic Markov Chain and Generate a Random Spanning Tree of a Directed Graph
• Moore-penrose inverse of the incidence matrix of a tree
• Distances in Weighted Trees and Group Inverse of Laplacian Matrices
• A Characterization and Representation of the Drazin Inverse
• Estimating a probability using finite memory
• Moore-penrose involutions in the classes of laplacians and simplices
• Doubly stochastic graph matrices, II
• Limits and the Index of a Square Matrix
• The representation and approximation for Drazin inverse
• A characterization of the Drazin inverse

This page was built for publication: Forest matrices around the Laplacian matrix