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第14回AIツール入門講座
「Google Colaboratoryによる
ネットワーク分析入門」
5. ネットワーク生成モデル
スケールフリー、スモールワールドなどのネットワーク生成モデ
ルについて説明します。
実ネットワークと人工ネットワーク
• 実ネットワーク
• 現実世界やSNSなどから観測
• 似たようなものを作るのが困難
• 人工ネットワーク
• モデルに基づいて生成
• 数学的な解析が比較的容易
モデル
化 検証
人工ネットワークの例
• 次数分布の比較
ランダム
グラフ
スケール
フリー
グラフ
完全
グラフ
空手
クラブ
X軸:次数
Y軸:頻度
スケールフリーグラフ
• 成長:頂点が新たに追加され、減ることはない
• 優先的選択:新たに追加される頂点は、次数の高い頂点と高い
確率で辺で結ばれる
に基づく生成モデル
• X軸とY軸を対数目盛にした両対数グラフで
次数分布が直線になる
スケールフリーグラフの例
• 頂点数1000
• 新たな頂点は、既存の頂点と3本の辺でつながる
平均次数:6
両対数グラフ
で直線
スモールワールドグラフ
• 「6次のつながり」
• 友達の友達の…と6回たどると、任意の2人の米国人がつながる
• 頂点の数に比べて、頂点間の距離は驚くほど小さい
• クラスタ係数が大きく、かつ平均頂点間距離が短いグラフの生
成モデル
クラスタ係数と平均頂点間距離
• (円周上の近傍とつながる)規則的なグラフの辺をつなぎ変える
平均頂点間距離
クラスタ係数

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