  We present a study of the distribution of AGN in clusters of galaxies with a
uniformly selected, spectroscopically complete sample of 35 AGN in eight
clusters at z = 0.06 to 0.31. We find that the 12 AGN with L_X > 10^42 erg/s in
galaxies more luminous than a rest-frame M_R < -20 mag are more centrally
concentrated than typical cluster galaxies of this luminosity, although these
AGN have comparable velocity and substructure distributions to other cluster
members. In contrast, a larger sample of 30 cluster AGN with L_X > 10^41 erg/s
do not show evidence for greater concentration than inactive members, nor
evidence for a different kinematic or substructure distribution. As we do see
clear differences in the spatial and kinematic distributions of the blue
Butcher-Oemler and red galaxy populations, any difference in the AGN and
inactive galaxy population must be less distinct than that between these two
pairs of populations. Comparison of the AGN fraction selected via X-ray
emission in this study to similarly-selected AGN in the field indicates that
the AGN fraction is not significantly lower in clusters, contrary to AGN
identified via visible-wavelength emission lines, but similar to the
approximately constant radio-selected AGN fraction in clusters and the field.
We also find significant evidence for variation between clusters and explore
the dependence of cluster AGN fraction on redshift, velocity dispersion,
cluster substructure, and Butcher-Oemler fraction. While we see weak evidence
for several trends, correlations between these four parameters in our small
sample precludes identification of which one(s) most strongly influence the
cluster AGN fraction.
