Networking

Line Orthogonality in Adjacency Eigenspace With Application to Community Partition

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Executive Summary

Different from Laplacian or normal matrix, the properties of the adjacency eigenspace received much less attention. Recent work showed that n-odes projected into the adjacency eigenspace ex-hibit an orthogonal line pattern and nodes from the same community locate along the same line. In this paper, the authors conduct theoretical studies based on graph perturbation to demonstrate why this line orthogonality property holds in the adjacency eigenspace and why it generally disappears in the Laplacian and normal eigenspaces.

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