  We find a significant anti-correlation between the hard X-ray photon index
and the Eddington ratio L_Bol/L_Edd for a sample of Low-Ionization Nuclear
Emission-line Regions (LINERs) and local Seyfert galaxies, compiled from
literatures with Chandra or XMM-Newton observations. This result is in contrast
with the positive correlation found in luminous active galactic nuclei (AGNs),
while it is similar to that of X-ray binaries (XRBs) in low/hard state. Our
result is qualitatively consistent with the spectra produced from advection
dominated accretion flows (ADAFs). It implies that the X-ray emission of
low-luminosity active galactic nuclei (LLAGNs) may originate from the
Comptonization process in ADAF, and the accretion process in LLAGNs may be
similar to that of XRBs in the low/hard state, which is different from that in
luminous AGNs.
