  We consider highly heterogeneous random networks with symmetric interactions
in the limit of high connectivity. A key feature of this system is that the
spectral density of the corresponding ensemble exhibits a divergence within the
bulk. We study the structure of the eigenvectors associated with this
divergence and find that they are multifractal with the statistics of
eigenvector elements matching those of the resolvent entries. The corresponding
localization mechanism relies on the statistical properties of the nodes rather
than on any spatial structure around a localization centre. This "statistical
localization" mechanism is potentially relevant for explaining localization in
different models that display singularities in the bulk of the spectrum of
eigenvalues
