2003.05.27
LINKED: The New Science of Networks
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．
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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