社群網絡偵測之相鄰矩陣轉換

社群網絡分析 (social network analysis，簡稱 SNA) 是一種對社群網絡進行系統性的量化分析方法，網絡分析研究的關鍵即是網絡主體間的關係數據，而關係數據以矩陣形式儲存為相鄰矩陣 (adjacency matrix)。若僅考量形式單一且量化關係選擇主觀的相鄰矩陣，可能忽略網絡潛藏訊息。因此，在進行網絡分析前，可充分利用相鄰矩陣，對網絡主體間的關係進行轉換，以放大網絡關係的強或弱。本文所提出的方法，利用了相鄰矩陣中所提供的多重訊息，可建構相同社群下的多個關係矩陣 (proximity matrix)。每個關係矩陣採取不同的角度量化網絡主體間的關係，各具不同的含意。本文採用探索式資料分析工具廣義相關圖 (generalized association plots, Chen, 2002; Wu et al., 2010) 搭配橢圓排序方法 (elliptical seriation algorithm) ，對轉換後的關係矩陣進行社群網絡分析，並對於不同的關係矩陣在 GAP 分析下的結果，解釋分群的品質與結構。另一方面，本文參考了社群網絡分析方法 Girvan-Newman 演算法 (Girvan-Newman algorithm, Girvan and Newman, 2002)，對原始相鄰矩陣進行分析，以此進一步比較相鄰矩陣轉換的前後以及在相異的分析方法下，所得社群模組性 (modularity of community, Newman 2004) 以及社群結構的異同。

關鍵字

社群網絡分析；廣義相關圖；關係矩陣；橢圓排序演算法； Girvan-Newman 演算法；相鄰矩陣；模組性；邊中介性

並列摘要

Social network analysis (SNA) provides a systematic method to uncover social network structures. One of the main components of SNA is the adjacency matrix, which carries information about the relationship between pairs of vertices in a network. This thesis work presents an approach that can help to strengthen this information. By simple operations on the adjacency matrix, proximity matrices are created. Each proximity matrix quantifies the relationship between pairs of vertices from a different point of view. With the use of the proximity matrices, additional information may be retrieved. To detect community structures from the proximity matrices, the elliptical seriation algorithm (Chen, 2002) implemented in GAP (generalized association plots, Chen, 2002) is considered, which is a java-designed exploratory data analysis (EDA) software. The performance of GAP is compared to that of the Girvan-Newman algorithm (Girvan and Newman, 2002). Community structures detected by the two algorithms are evaluated and examined.

並列關鍵字

Social network analysis, SNA ； Generalized association plots, GAP ； Elliptical seriation algorithm ； Pearson’s correlation coefficient ； Proximity matrix ； Girvan-Newman algorithm ； Adjacency matrix ； Modularity ； Edge betweenness

參考文獻

[5] Girvan; M.; & Newman; M. E. J. (2002). Community structure in social and biological networks. Proceedings of the National Academy of Sciences; 99(12); 7821-7826. doi: 10.1073/pnas.122653799

[6] Girvan; M.; & Newman; M. E. J. (2004). Finding and evaluating community structure in networks. Phys Rev E Stat Nonlin Soft Matter Phys; 69(2 Pt 2); 026113.

[7] Leicht; E. A.; & Newman; M. E. J. (2002). Community Structure in Directed Networks. Physical Review Letters; 100(11); 118703.

[8] Newman; M. E. J. (2004). Analysis of weighted networks. Phys Rev E Stat Nonlin Soft Matter Phys; 70(5 Pt 2).

[9] Newman; M. E. J. (2006). Modularity and community structure in networks. Proceedings of the National Academy of Sciences; 103(23); 8577-8582. doi: 10.1073/pnas.0601602103

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社群網絡偵測之相鄰矩陣轉換

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