Mathematical Modeling of Complex Networks by Using a Learning Approach

本研究的目的是分析不断快速增长的互联网这个复杂的网络，为不断增长的网络寻找数学模型，并用数学模型来解释其行为。首先提出了一种从社交网络数据中提取社区的方法。其次，在定义了社交网络中信息扩散的影响最大化问题后，我们提出了一种利用bond-percolation的快速求解方法。最后，我们提出了一种估计网络增长可能的链路生成的方法。在实际的大规模网络中对所提出的方法进行了评估。

The aim of this research is to analysis the Internet which keeps growing rapidly as a complex network, to find a mathematical model for the growing network, and to explain its behavior by using the mathematical model. Firstly we proposed a method which extracts communities from social network data. Secondly, after defining an influence maximization problem for information diffusion in a social network, we proposed a very fast method to solve the problem by making good use of bond-percolation. Finally, we proposed a method which estimates probable link generations for network growth. All the proposed methods were evaluated for real large-scale networks.