  The discovery of novel topological phase advances our knowledge of nature and
stimulates the development of applications. In non-Hermitian topological
systems, the topology of band touching exceptional points is very important.
Here we propose a real-energy topological gapless phase arising from
exceptional points in one dimension, which has identical topological invariants
as the topological gapless phase arising from degeneracy points. We develop a
graphic approach to characterize the topological phases, where the eigenstates
of energy bands are mapped to the graphs on a torus. The topologies of
different phases are visualized and distinguishable; and the topological
gapless edge state with amplification appropriate for topological lasing exists
in the nontrivial phase. These results are elucidated through a non-Hermitian
Su-Schrieffer-Heeger ladder. Our findings open new way for identifying topology
phase of matter from visualizing the eigenstates.
