応用数理
Online ISSN : 2432-1982
論文
ハイパーグラフ上の熱とそのネットワーク解析への応用
池田 正弘
著者情報
ジャーナル フリー

2021 年 31 巻 2 号 p. 2-10

詳細
抄録

In the present paper, I review our recent two papers of the joint works with Atsushi Miyauchi (Tokyo Univ.), Yuuki Takai(KIT) and Yuichi Yoshida (NII). I mainly introduce the background of their papers and the fundamental notions for community detection of networks. First I review the notion of Laplacian and Cheegerʼs inequality for the usual undirected graph. After that, I introduce the definition of the (submodular) Laplacian for hypergraphs and the heat on them. Especially, I introduce several properties of the Laplacian and heat such as maximal monotonicity of the Laplacian and well-definedness of the heat and the Personalized PageRank respectively. Moreover, I introduce the application of the properties to the community detection on hypergraphs.

著者関連情報
© 2021日本応用数理学会
前の記事 次の記事
feedback
Top