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arXiv · 1505.07543

Localized eigenvectors of the non-backtracking matrix

Tatsuro Kawamoto
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Abstract

In the case of graph partitioning, the emergence of localized eigenvectors can cause the standard spectral method to fail. To overcome this problem, the spectral method using a non-backtracking matrix was proposed. Based on numerical experiments on several examples of real networks, it is clear that the non-backtracking matrix does not exhibit localization of eigenvectors. However, we show that localized eigenvectors of the non-backtracking matrix can exist outside the spectral band, which may lead to deterioration in the performance of graph partitioning.

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Tatsuro Kawamoto. 2016-02-08. Localized eigenvectors of the non-backtracking matrix. https://arxiv.org/abs/1505.07543

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