  In this work, the outward and inward accessibilities of individual nodes are
defined and their potential for application is illustrated with respect to the
investigation of 6 different types of networks. The outward accessibility
quantifies the potential of an individual node for accessing other nodes
through random walks. The inward accessibility measures the potential of a
given node of being accessed by other nodes. Both the inward and outward
accessibilities are measured with respect to successive time steps along the
walks, providing an interesting means for the characterization of the transient
non-linear dynamics of accessibility. Self-avoiding walks are considered here
because they are more purposive and necessarily finite (unlike traditional
random walks). The results include the identification of the fact that the
inward values tend to be much smaller than the outward values, the tendency of
the inward accessibility to be highly correlated with the node degree while the
outward values are mostly uncorrelated with that measurements, the distinct
behavior of the accessibility in geographical networks, the dominance of hubs
in scale free networks, as well as the enhanced uniformity of the
accessibilities for the path-regular model. Also investigated was the
possibility to predict the accessibility of a given node in terms of its
respective degree. The concepts of inward and outward accessibility, as well as
the several obtained results, have several implications and potential for
applications to several real-time problems including disease spreading, WWW
surfing, protein interaction, cortical networks and network attacks, among
others.
