The Deformed Graph Laplacian and Its Applications to Network Centrality Analysis

DOI10.1137/17M1112297zbMath1381.05043MaRDI QIDQ4604568

Vanni Noferini, Peter Grindrod, Desmond J. Higham

Publication date: 2 March 2018

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

generating functionmatrix polynomialcomplex networkcentrality indexdeformed graph Laplaciannonbacktracking

Mathematics Subject Classification ID

Small world graphs, complex networks (graph-theoretic aspects) (05C82) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Matrices over function rings in one or more variables (15A54) Special matrices (15B99)

Related Items

Three conjectures of Ostrander on digraph Laplacian eigenvectors ⋮ Matching number, Hamiltonian graphs and magnetic Laplacian matrices ⋮ On the exponential generating function for non-backtracking walks ⋮ There is no going back: properties of the non-backtracking Laplacian ⋮ Weighted Enumeration of Nonbacktracking Walks on Weighted Graphs ⋮ Geometric and spectral analysis on weighted digraphs ⋮ Node and Layer Eigenvector Centralities for Multiplex Networks ⋮ Beyond non-backtracking: non-cycling network centrality measures ⋮ Efficient Weingarten map and curvature estimation on manifolds ⋮ Non-Backtracking Alternating Walks ⋮ Non-backtracking PageRank ⋮ Dynamic Katz and related network measures ⋮ A Theory for Backtrack-Downweighted Walks ⋮ Eigenvalues of the non-backtracking operator detached from the bulk

Uses Software

• CONTEST
• testmatrix

Cites Work

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