  The measurement called accessibility has been proposed as a means to quantify
the efficiency of the communication between nodes in complex networks. This
article reports important results regarding the properties of the
accessibility, including its relationship with the average minimal time to
visit all nodes reachable after $h$ steps along a random walk starting from a
source, as well as the number of nodes that are visited after a finite period
of time. We characterize the relationship between accessibility and the average
number of walks required in order to visit all reachable nodes (the exploration
time), conjecture that the maximum accessibility implies the minimal
exploration time, and confirm the relationship between the accessibility values
and the number of nodes visited after a basic time unit. The latter
relationship is investigated with respect to three types of dynamics, namely:
traditional random walks, self-avoiding random walks, and preferential random
walks.
