  We investigate how in complex systems the eigenpairs of the matrices derived
from the correlations of multichannel observations reflect the cluster
structure of the underlying networks. For this we use daily return data from
the NYSE and focus specifically on the spectral properties of weight W_{ij} =
|C|_{ij} - \delta_{ij} and diffusion matrices D_{ij} = W_{ij}/s_j- \delta_{ij},
where C_{ij} is the correlation matrix and s_i = \sum_j W_{ij} the strength of
node j. The eigenvalues (and corresponding eigenvectors) of the weight matrix
are ranked in descending order. In accord with the earlier observations the
first eigenvector stands for a measure of the market correlations. Its
components are to first approximation equal to the strengths of the nodes and
there is a second order, roughly linear, correction. The high ranking
eigenvectors, excluding the highest ranking one, are usually assigned to market
sectors and industrial branches. Our study shows that both for weight and
diffusion matrices the eigenpair analysis is not capable of easily deducing the
cluster structure of the network without a priori knowledge. In addition we
have studied the clustering of stocks using the asset graph approach with and
without spectrum based noise filtering. It turns out that asset graphs are
quite insensitive to noise and there is no sharp percolation transition as a
function of the ratio of bonds included, thus no natural threshold value for
that ratio seems to exist. We suggest that these observations can be of use for
other correlation based networks as well.
