確率モデルに基づく複雑ネットワークの統計的分析手法に関する研究

摘要

We study on complex networks, which are backbones of various complex systems and have recently attracted a lot of attention in many research fields. First, a nongrowing network generation model is analyzed by using statistical mechanical techniques. Secondly, we propose an improved algorithm for belief propagation, which is frequently used in probabilistic reasoning problems. The improved algorithm is based on the heterogeneity of complex networks, and can be decrease the number of iterative calculation. Thirdly, a new community detection algorithm is proposed, which is based on a concept of nonadditive volume. These works will give a fundamental base for research on complex networks and be useful for future research.%脳において大量のニューロンが作るシステム，イ ンターネットのような大規模な工学的システム，そ して企業間の取引関係などは，どれも数多くの構成 要素が相互作用しあっている複雑なシステムである．