  The limited penetrable horizontal visibility graph algorithm was recently
introduced to map time series in complex networks. We extend this visibility
graph and create a directed limited penetrable horizontal visibility graph and
an image limited penetrable horizontal visibility graph. We define the two
algorithms and provide theoretical results on the topological properties of
these graphs associated with different types of real-value series (or
matrices). We perform several numerical simulations to further check the
accuracy of our theoretical results. Finally we present an application of the
directed limited penetrable horizontal visibility graph for measuring
real-value time series irreversibility, and an application of the image limited
penetrable horizontal visibility graph that discriminates noise from chaos. The
empirical results show the effectiveness of our proposed algorithms.
