| Summary: | 碩士 === 國立臺灣大學 === 資訊工程學研究所 === 96 === The small world phenomenon, the principle that most of people are linked by short chains of acquaintances, is first studied as a problem in social science. It is also
a feature of a range of networks arising in nature and technology. Early experiments showed that it has two properties: first, short chains are widespread, and second,
individuals with local information are able to find the chains. Kleinberg proposed a family of network models and a greedy algorithm, showing that there is a unique model within the family for which the greedy algorithm’s running time is O(log2 N). We study Kleinberg’s theorems and give some models based on Kleinberg’s family:torus, grids of high dimension, and cube.
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