2023 Fiscal Year Final Research Report
Development of a Reduced Representation of Adjacency Matrices in Complex Networks and Its Applications
| Project/Area Number |
21K03387
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
岡部 拓也 静岡大学, 工学部, 准教授 (10324336)
伊東 啓 長崎大学, 熱帯医学研究所, 准教授 (80780692)
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| Project Period (FY) |
2021-04-01 – 2024-03-31
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| Keywords | ネットワーク科学 / 社会ネットワーク / 複雑ネットワーク / 次数相関 / 隣接行列 / クラスター |
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| Outline of Final Research Achievements |
This research aims to address the challenge of managing the adjacency matrices of extremely large networks by developing a reduced representation of these matrices. We focus on social networks involving contact and movement as our primary target. Specifically, we concentrate on the spread of infectious diseases within social networks and attempt to reduce the network based on the basic and type reproduction numbers used in mathematical epidemiology. These findings have been published in two papers. Additionally, an analysis incorporating inter-regional migration using real data was also published. In the final year of the project, we devised a simplified method for representing degree correlations through eigenvalue decomposition and applied it to various social network data.
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| Free Research Field |
非線形物理学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究の隣接行列の縮約的表現法は，巨大な隣接行列を現実的に扱うための一つの有効な手段を提供する．この方法論は，感染症の拡散モデルだけでなく，情報伝達ネットワークにも適用可能で，その応用範囲は非常に広い．特に固有値分解の手法が2部グラフでは特異値分解として適用される点が特徴的で，これにより二部グラフ構造を持つデータセットの解析に使える．また，本研究の成果は，現在注目されている推薦システムにも応用可能と期待でき，ユーザの嗜好に基づいたコンテンツ推薦やマーケットバスケット解析等、多岐にわたる分野での利用が期待できる。以上のように，本研究はネットワーク科学の発展に寄与し，社会的意義も非常に大きい．
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