  We investigate adjacency matrices of bipartite graphs with power-law degree
distribution. Motivation for this study is twofold. First, vibrational states
in granular matter and jammed sphere packings; second, graphs encoding social
interaction, especially electronic commerce. We establish the position of the
mobility edge, and show that it strongly depends on the power in the degree
distribution and on the ratio of the sizes of the two parts of the bipartite
graph. At the jamming threshold, where the two parts have the same size,
localization vanishes. We found that the multifractal spectrum is non-trivial
in the delocalized phase, but still near the mobility edge. We also study an
empirical bipartite graph, namely the Amazon reviewer-item network. We found
that in this specific graph mobility edge disappears and we draw a conclusion
from this fact regarding earlier empirical studies of the Amazon network.
