  The AMIGA project aims to build a well defined and statistically significant
reference sample of isolated galaxies in order to estimate the environmental
effects on the formation and evolution of galaxies. The goal of this paper is
to provide a measure of the environment of the isolated galaxies in the AMIGA
sample, quantifying the influence of the candidate neighbours identified in our
previous work and their potential effects on the evolution of the primary
galaxies. Here we provide a quantification of the isolation degree of the
galaxies in this sample. Our starting sample is the Catalogue of Isolated
Galaxies (CIG). We used two parameters to estimate the influence exerted by the
neighbour galaxies on the CIG galaxy: the local number density of neighbour
galaxies and the tidal strength affecting the CIG galaxy. We show that both
parameters together provide a comprehensive picture of the environment. For
comparison, those parameters have also been derived for galaxies in denser
environments such as triplets, groups and clusters. The CIG galaxies show a
continuous spectrum of isolation, as quantified by the two parameters, from
very isolated to interacting. The fraction of CIG galaxies whose properties are
expected to be influenced by the environment is however low (159 out of 950
galaxies). The isolated parameters derived for the comparsion samples gave
higher values than for the CIG and we found clear differences for the average
values of the 4 samples considered, proving the sensitivity of these
parameters. The environment of the galaxies in the CIG has been characterised,
using two complementary parameters quantifying the isolation degree, the local
number density of the neighbour galaxies and the tidal forces affecting the
isolated galaxies. (Abridged)
