2003.05.27

LINKED: The New Science of Networks

Albert-Laszlo Barabasi. LINKED: The New Science of Networks(新ネットワーク思考 - 世界のしくみを読み解く), 2002
コミュニティを考えるうえで極めて重要となる一冊.サーベイとしても強力.以下は研究室ミーティングでのレジュメ.
・ランダムネットワークの相転移(p.30)
巨大クラスタを生み出すための「ノードあたりの平均リンク数」の閾値は1
・Small WorldとSix Degrees of Separation(p.46)
ノード間距離dの計算式:d=log N / log k(N: 総ノード数,k: 平均リンク数)
Webの直径は18.59(1998)
直径はノード間の経路の最大値を示す.
・弱い紐帯(p.65)
完全グラフをコミュニティ(=クラスタ)とみなす.
社会ネットワークはクラスタが弱い紐帯で結ばれているような形態.
クラスタリング係数:自分から1パスの人々の間で結ばれるリンク数/最大リンク数
ランダムネットワークでは指数関数的に減少するが,現実のネットワーク(Small World)では0.5程度.
・スケールフリーネットワーク(p.100)
現実のネットワークにおいてはリンク数の分布は正規分布・ポアソン分布にはならない.
ベキ法則N(k) = k^(-r)に類似(N(k):リンク数がkであるようなノードの総数,rは2〜3).
莫大なリンクを持つノード=ハブの存在を許す.
・スケールフリーネットワークの生成過程(p.126)
成長と優先的選択:新しいノードは多くのリンクを持つノードにリンクを張る.
→古いノードほど成長する.
適応度の導入:何らかの評価値を導入し,適応度×リンク数で優先的選択を行うと逆転モデル(ex. gooとgoogle)を記述できる.(p.137)
・スケールフリーネットワークの特徴(p.170)
現実のネットワークはランダムなエラーに対してロバスト.ハブを狙った攻撃に対して脆弱.
・有向リンクの限界(p.238)
リボン型モデル:IN大陸,中央大陸,OUT大陸,半島,島,トンネル
任意のノードから全てのリンクに到達することはできない.

Posted by i2k at 2003.05.27 05:27 PM

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