Question: Spectral Clustering - Consider an undirected graph with non-negative edge weights w ij and graph Laplacian L. Suppose there are m connected components A 1

Spectral Clustering -

Consider an undirected graph with non-negative edge weights wij and graph Laplacian L. Suppose

there are m connected components A1,A2,..,Am in the graph.

Show that there are m eigenvectors of L corresponding to eigenvalue zero, and the indicator vectors of these components IA1,...,IAm span

the zero eigenspace.

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