  This paper presents a concise tutorial on spectral clustering for broad
spectrum graphs which include unipartite (undirected) graph, bipartite graph,
and directed graph. We show how to transform bipartite graph and directed graph
into corresponding unipartite graph, therefore allowing a unified treatment to
all cases. In bipartite graph, we show that the relaxed solution to the $K$-way
co-clustering can be found by computing the left and right eigenvectors of the
data matrix. This gives a theoretical basis for $K$-way spectral co-clustering
algorithms proposed in the literatures. We also show that solving row and
column co-clustering is equivalent to solving row and column clustering
separately, thus giving a theoretical support for the claim: ``column
clustering implies row clustering and vice versa''. And in the last part, we
generalize the Ky Fan theorem---which is the central theorem for explaining
spectral clustering---to rectangular complex matrix motivated by the results
from bipartite graph analysis.
