Many astrophysical models predict a diffuse flux of high-energy neutrinos from active galactic nuclei and other extragalactic sources. At muon energies above 1 TeV, the upward-going muon flux induced by neutrinos from active galactic nuclei is expected to exceed the flux due to atmospheric neutrinos. We have performed a search for this astrophysical neutrino flux by looking for upward-going muons in the highest energy data sample from the Super-Kamiokande detector using 1679.6 live days of data. We found one extremely high energy upward- going muon event, compared with an expected atmospheric neutrino background of 0.46 +/- 0.23 events. Using this result, we set an upper limit on the diffuse flux of upward- going muons due to neutrinos from astrophysical sources in the muon energy range 3.16-100 TeV.
