Graph eigenvectors, fundamental weights and centrality metrics for nodes in networks
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Summary
The set of such nodal centrality metrics, the squared eigenvector components of the adjacency matrix over all eigenvalue λ_k for each node j, is 'ideal' in the sense of being complete, uncorrelated and mathematically precisely defined and computable.
- Type
- preprint
- Published
- 2014-01-18
- Cited by
- 31
- References
- 40
- Access
- Open access
- OpenAlex
- https://openalex.org/W2157995998
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:7041278
Keywords
Lambda, Combinatorics, Eigenvalues and eigenvectors, Adjacency matrix, Mathematics
References
- Two new graph-theoretical methods for generation of eigenvectors of chemical graphs
- Measuring Robustness of Complex Networks
- Complex Networks: Structure and Dynamics
- Matrix Analysis and Applied Linear Algebra
- Performance Analysis of Complex Networks and Systems
- Principal eigenvectors of irregular graphs
- Algebraic connectivity of graphs
- Graph Spectra for Complex Networks
- Epidemic processes in complex networks
- On Hadamard diagonalizable graphs
- A spectral condition for odd cycles in graphs
- On the spectral radius of graphs
- Random matrices: Universality of local eigenvalue statistics
- Consistency of spectral clustering
- Epidemic phase transition of the SIS type in networks
- Eigenspaces for Graphs
- New Lower Bounds for the Fundamental Weight of the Principal Eigenvector in Complex Networks
- Robustness surfaces of complex networks
- Some results on graph spectra
- Induced, endogenous and exogenous centrality
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- Spectral approaches for identifying kinetic features in molecular dynamics simulations of globular proteins
- Analysis of the Robustness Dynamics of Wireless Mobile Ad Hoc Networks via Time Varying Dual Basis Representation
- New Lower Bounds for the Fundamental Weight of the Principal Eigenvector in Complex Networks
- Correlation between centrality metrics and their application to the opinion model
- Dynamic state determination of a software-defined network via dual basis representation
- Orthogonal Eigenvector Matrix of the Laplacian
- Approximating frustration scores in complex networks via perturbed Laplacian spectra
- A Positional Approach for Network Centrality
- Integrating cross-frequency and within band functional networks in resting-state MEG: A multi-layer network approach
- Universality of the SIS prevalence in networks
- A New Metric to Find the Most Vulnerable Node in Complex Networks
- Controllability of Networks of Linear Systems: a Graph Theoretic Approach
- New bounds on the spectral radius of graphs based on the moment problem
- Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra
- Recovery of eigenvectors from eigenvalues in systems of coupled harmonic oscillators
- Measure-theoretic bounds on the spectral radius of graphs from walks
- Optimal Portfolio Choice and Stock Centrality for Tail Risk Events
- Eigenvectors from eigenvalues in quaternion matrix with computer realization
- Discovering Important Nodes of Complex Networks Based on Laplacian Spectra
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