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Abstract: Small-world networks are networks in which the graphical diameter of thenetwork is as small as the diameter of random graphs but whose nodes are highlyclustered when compared with the ones in a random graph. Examples ofsmall-world networks abound in sociology, biology, neuroscience and physics aswell as in human-made networks. This paper analyzes the average delivery timeof messages in dense small-world networks constructed on a plane. Iterativeequations for the average message delivery time in these networks are providedfor the situation in which nodes employ a simple greedy geographic routingalgorithm. It is shown that two network nodes communicate with each other onlythrough their short-range contacts, and that the average message delivery timerises linearly if the separation between them is small. On the other hand, iftheir separation increases, the average message delivery time rapidly saturatesto a constant value and stays almost the same for all large values of theirseparation.



Author: Hazer Inaltekin, Mung Chiang, Harold Vincent Poor

Source: https://arxiv.org/







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