複雑なネットワークの自己類似性
Chaoming Song1, Shlomo Havlin, Hernán A Makse
1Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA.
Nature
|January 28, 2005
まとめ
複雑なネットワークは,すべてのスケールで自己繰り返しのパターンを示し,以前の仮定に挑戦します. この発見は,有限の自己類似指数を明らかにし,それらのスケールフリーな性質を説明し,普遍的な自己組織化ダイナミクスを示唆しています.
科学分野:
- ネットワーク科学 ネットワーク科学
- 統計物理学 統計物理
- 複雑なシステム 複雑なシステム
背景:
- インターネットや生物学的システムを含む複雑なネットワークは,しばしばスケールフリーであり,パワー・ローの度数分布を示しています.
- 現存する理論では,複雑なネットワークは,その小さな世界の性質のために,長度スケールの変換下で不変性を欠いていることを示唆している.
- この自己類似性の欠如は,フラクタル構造や自己類似構造の期待される行動と矛盾している.
研究 の 目的:
- 現実世界の複雑なネットワークのスケール不変性と自己類似性を調査する.
- 複雑なネットワークは,異なる長さのスケールで自己類似ではないという支配的な見解に異議を唱えるために.
- 複雑なネットワークの構造と組織を統制する基本的な性質を特定する.
主な方法:
- 様々な現実世界の複雑なネットワークの分析.
- 粗い粒子を様々なサイズの箱に詰め込み,レノルマライゼーション手順を適用する.
- スケール指数を決定するために,箱の数と箱サイズとの関係の定量化.
主要な成果:
- 以前の考えに反して,複雑なネットワークは,すべての長さのスケールで自己繰り返しのパターンを示します.
- ネットワークをカバーするために必要な箱の数とこれらの箱のサイズとの間の力法関係が特定されました.
- これらの複雑なネットワークに対して,有限の自己類似指数を決定した.
結論:
- 複雑なネットワークは固有の自己類似性を示し,有限なスケーリング指数によって特徴付けられます.
- 特定された自己類似性は,多くの現実世界のネットワークの観測されたスケールフリー特性の根本的な説明を提供します.
- これらの発見は,複雑なネットワーク構造の形成を駆動する共通の基礎的な自己組織化メカニズムを示唆しています.
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