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In this work, the outward and inward accessibilities of individual nodes aredefined and their potential for application is illustrated with respect to theinvestigation of 6 different types of networks. The outward accessibilityquantifies the potential of an individual node for accessing other nodesthrough random walks. The inward accessibility measures the potential of agiven node of being accessed by other nodes. Both the inward and outwardaccessibilities are measured with respect to successive time steps along thewalks, providing an interesting means for the characterization of the transientnon-linear dynamics of accessibility. Self-avoiding walks are considered herebecause they are more purposive and necessarily finite (unlike traditionalrandom walks). The results include the identification of the fact that theinward values tend to be much smaller than the outward values, the tendency ofthe inward accessibility to be highly correlated with the node degree while theoutward values are mostly uncorrelated with that measurements, the distinctbehavior of the accessibility in geographical networks, the dominance of hubsin scale free networks, as well as the enhanced uniformity of theaccessibilities for the path-regular model. Also investigated was thepossibility to predict the accessibility of a given node in terms of itsrespective degree. The concepts of inward and outward accessibility, as well asthe several obtained results, have several implications and potential forapplications to several real-time problems including disease spreading, WWWsurfing, protein interaction, cortical networks and network attacks, amongothers.

Inward and Outward Node Accessibility in Complex Networks as Revealed by Non-Linear Dynamics