Navigability on Networks: A Graph Theoretic Perspective

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Human navigation has been of interest to psychologists and cognitive scientists since the past few decades. It was in the recent past that a study of human navigational strategies was initiated with a network analytic approach, instigated mainly by Milgrams small world experiment. We brief the work in this direction and provide answers to the algorithmic questions raised by the previous study. It is noted that humans have a tendency to navigate using centers of the network - such paths are called the center-strategic-paths. We show that the problem of finding a center-strategic-path is an easy one. We provide a polynomial time algorithm to find a center-strategic-path between a given pair of nodes. We apply our finding in empirically checking the navigability on synthetic networks and analyze few special types of graphs.