Fractality and long-range degree correlation in complex networks

2021 Fiscal Year Final Research Report

• Project/Area Number: 19K03646
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Hokkaido University
• Principal Investigator: Yakubo Kousuke 北海道大学, 工学研究院, 教授 (40200480)
• Co-Investigator(Kenkyū-buntansha): 小布施 秀明 北海道大学, 工学研究院, 助教 (50415121)
• Project Period (FY): 2019-04-01 – 2022-03-31
• Keywords: 複雑ネットワーク / フラクタル / 長距離次数相関

Outline of Final Research Achievements

Many complex networks exhibit fractality in a topological sense. It is well known that the mechanism of this property is closely related to self-organized criticality. In this study, however, another mechanism of fractality in networks is explored by clarifying the relationship between fractality and the correlation between the number of neighboring nodes of each node (degree). Specifically, we propose mathematical models of fractal complex networks based on self-organized critical dynamics and reveal how fractality is generated from the long-range degree correlation by elucidating the relationship between fractality and the empirical fact that high degree nodes (hubs) are far away from each other.

Free Research Field

物理学

Academic Significance and Societal Importance of the Research Achievements

海岸線などの通常のフラクタル系の形成機構を自己組織化臨界性に基づくモデルにより理解しようとする試みは従来から行われてきたが、ユークリッド距離が定義されないネットワーク系におけるトポロジカルな意味でのフラクタル性も同じ機構で説明され得ることを示すことは複雑系の理解に大きな進展をもたらす。また、この性質を長距離次数相関の観点から解明する試みは前例を見ないものであり、得られた知見は機能性ネットワークのボトムアップ的デザインにも大きなインパクトを与える。