Average message delivery time for small-world networks in the continuum limit

12 years 11 months ago

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Small-world networks are networks in which the graphical diameter of the network is as small as the diameter of random graphs but whose nodes are highly clustered when compared with the ones in a random graph. Examples of small-world networks abound in sociology, biology, neuroscience and physics as well as in human-made networks such as the Internet, power grids and businesses. This paper analyzes the average delivery time of messages in dense small-world networks constructed on metric-measure spaces. Iterative equations for the average message delivery time in these networks are provided for the situation in which nodes employ a simple greedy geographic routing algorithm. It is shown that two network nodes communicate with each other only through their short-range contacts, and that the average message delivery time rises linearly if the separation between them is small. On the other hand, if their separation increases, the average message delivery time rapidly saturates to a constan...

Hazer Inaltekin, Mung Chiang, H. Vincent Poor

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