  A chordless cycle (induced cycle) $C$ of a graph is a cycle without any
chord, meaning that there is no edge outside the cycle connecting two vertices
of the cycle. A chordless path is defined similarly. In this paper, we consider
the problems of enumerating chordless cycles/paths of a given graph $G=(V,E),$
and propose algorithms taking $O(|E|)$ time for each chordless cycle/path. In
the existing studies, the problems had not been deeply studied in the
theoretical computer science area, and no output polynomial time algorithm has
been proposed. Our experiments showed that the computation time of our
algorithms is constant per chordless cycle/path for non-dense random graphs and
real-world graphs. They also show that the number of chordless cycles is much
smaller than the number of cycles. We applied the algorithm to prediction of
NMR (Nuclear Magnetic Resonance) spectra, and increased the accuracy of the
prediction.
