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Communication Dans Un Congrès Année : 2020

Comparing Spectra of Graph Shift Operator Matrices

Résumé

Typically network structures are represented by one of three different graph shift operator matrices: the adjacency matrix and unnormalised and normalised Laplacian matrices. To enable a sensible comparison of their spectral (eigenvalue) properties, an affine transform is first applied to one of them, which preserves eigengaps. Bounds, which depend on the minimum and maximum degree of the network, are given on the resulting eigenvalue differences. The monotonicity of the bounds and the structure of networks are related. Bounds, which again depend on the minimum and maximum degree of the network, are also given for normalised eigengap differences, used in spectral clustering. Results are illustrated on the karate dataset and a stochastic block model. If the degree extreme difference is large, different choices of graph shift operator matrix may give rise to disparate inference drawn from network analysis; contrariwise, smaller degree extreme difference results in consistent inference.
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Dates et versions

hal-04447405 , version 1 (08-02-2024)

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Johannes Lutzeyer, Andrew Walden. Comparing Spectra of Graph Shift Operator Matrices. International Conference on Complex Networks and Their Applications, Dec 2019, Lisbonne, Portugal. pp.191-202, ⟨10.1007/978-3-030-36683-4_16⟩. ⟨hal-04447405⟩
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