| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 100 === ``Six degree of Separation'' told us: any two individuals, selected randomly from almost anywhere on the planet, can know each other via a chain of average no more than six intermediate acquaintances. There are more tens of millions of people around the world, but the social network is a small world. With the dramatic growth of the World Wide Web and the Internet, even the rise of the social network-Facebook, the distance between two people seems much shorter than before. Through the experiment result, on Facebook, any two individuals are connected in five steps or fewer, on average. The world seems smaller. In this thesis, we construct a dynamic random graph model to simulate Facebook.
We regard each user of Facebook as a vertex and the friendship between two users as an edge, and try to depict the pattern of the random graph as time being approximately infinity. In the process of the construction, we applied different probability distributions to adding new vertices and edges, and deleting existing vertices and edges. Based on the preferential attachment and the idea of the weaker tends to be weeded out, the model seems to conform with Facebook. Furthermore, we prove that the degree distribution satisfies the power-law, a common feature of the small world networks. Therefore, we conclude that Facebook is also a small world.
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