  We show that the definition of neighbor in Markov random fields as defined by
Besag (1974) when the joint distribution of the sites is not positive is not
well-defined. In a random field with finite number of sites we study the
conditions under which giving the value at extra sites will change the belief
of an agent about one site. Also the conditions under which the information
from some sites is equivalent to giving the value at all other sites is
studied. These concepts provide an alternative to the concept of neighbor for
general case where the positivity condition of the joint does not hold.
