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	加重モジュラリティ分析	重み付き媒介中心性
分野	ネットワーク分析	ネットワーク分析
系統	Machine learning	Machine learning
提唱年	2004	2010
提唱者	Newman, M. E. J.	Opsahl, T.; Agneessens, F.; Skvoretz, J. (extending Freeman 1977 and Brandes 2001)
種類	Community structure optimization on weighted graphs	Centrality measure (path-based)
原典	Newman, M. E. J. (2004). Analysis of weighted networks. Physical Review E, 70(5), 056131.	Opsahl, T., Agneessens, F., & Skvoretz, J. (2010). Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks, 32(3), 245–251.
別名	weighted modularity, weighted Q optimization, weighted network community detection, strength-based modularity	WBC, weighted shortest-path betweenness, edge-weighted betweenness, geodesic betweenness (weighted)
関連	5	6
概要	Weighted modularity analysis extends the classical Newman-Girvan modularity measure to networks where edges carry numeric strengths (frequencies, intensities, costs). By replacing binary adjacency with tie weights, it finds community partitions that reflect how densely interconnected subgroups are relative to what is expected under a weighted null model, yielding more nuanced groupings than unweighted approaches on data where edge strength varies meaningfully.	Weighted Betweenness Centrality extends Freeman's betweenness measure to edge-weighted graphs by routing shortest paths through a tunable transformation of edge weights. Nodes that sit on many high-value shortest paths receive high scores, identifying brokers and bridges in social, biological, and information networks where tie strength matters.