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Introduction of network analysis with Google Colaboratory -- Network Algorithms

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Introduction of network analysis with Google Colaboratory -- Network Algorithms

Data & Analytics
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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」 4. ネットワークアルゴリズム 経路探索やコミュニティ抽出など、ごく基本的なアルゴリズムに ついて説明します。
ネットワークアルゴリズム • 時間内ではとても紹介し切れません • 興味のある方はGeeksforGeeksあたりを参照してください • https://www.geeksforgeeks.org/graph-data-structure-and- algorithms/
経路探索 • 幅優先探索 (BFS) • 深さ優先探索 (DFS) 0 1 2 3
空手クラブネットでの幅優先探索 • 頂点0から探索→深さ3で全頂点に到達 ネットワーク分析で超有名なネットワーク
距離に応じて色を変えて表示 距離0:赤、距離1:青、距離2:水色…
ダイクストラ法(Dijkstra’s algorithm) • 各辺の長さが同一であれば、幅優先で最短経路を見つけられる • 各辺の長さが非負で同一でない場合は、ダイクストラ法で、与 えられた開始点から他の頂点への最短経路を見つけられる • 距離の見積もりの中で最短のものから確定して処理を進める 1 3 1 1 3 1 s t
ダイクストラ法の例
コミュニティ抽出 • 多くのネットワークは密な部分(コミュニティ)を含んでいる • 似た頂点集合を見つけて情報推薦をする • 全体の構造を俯瞰する • ネットワークを描画する • グラフ分割(数/サイズが既知) vs • コミュニティ抽出(数/サイズが未知) • “Community Detection in Graphs”, S. Fortunato, Physics Reports, Vol.486, Issues 3-5, pp.75-174, 2010.
モジュラリティ最適化とラベル伝搬によ るコミュニティ抽出 抽出手法をimportして使用 モジュラリティ最適化による結果 ラベル伝搬による結果

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