Department of Economics & Management, Université Saint-Louis-Bruxelles, Brussels, Belgium.
PLoS One. 2020 Dec 30;15(12):e0244377. doi: 10.1371/journal.pone.0244377. eCollection 2020.
In order to understand and represent the importance of nodes within networks better, most of the studies that investigate graphs compute the nodes' centrality within their network(s) of interest. In the literature, the most frequent measures used are degree, closeness and/or betweenness centrality, even if other measures might be valid candidates for representing the importance of nodes within networks. The main contribution of this paper is the development of a methodology that allows one to understand, compare and validate centrality indices when studying a particular network of interest. The proposed methodology integrates the following steps: choosing the centrality measures for the network of interest; developing a theoretical taxonomy of these measures; identifying, by means of Principal Component Analysis (PCA), latent dimensions of centrality within the network of interest; verifying the proposed taxonomy of centrality measures; and identifying the centrality measures that best represent the network of interest. Also, we applied the proposed methodology to an existing graph of interest, in our case a real friendship student network. We chose eighteen centrality measures that were developed in SNA and are available and computed in a specific library (CINNA), defined them thoroughly, and proposed a theoretical taxonomy of these eighteen measures. PCA showed the emergence of six latent dimensions of centrality within the student network and saturation of most of the centrality indices on the same categories as those proposed by the theoretical taxonomy. Additionally, the results suggest that indices other than the ones most frequently applied might be more relevant for research on friendship student networks. Finally, the integrated methodology that we propose can be applied to other centrality indices and/or other network types than student graphs.
为了更好地理解和表示网络中节点的重要性，大多数研究网络的文献都会计算节点在其感兴趣的网络中的中心性。在文献中，使用最频繁的度量标准是度数、接近度和/或中间中心度，即使其他度量标准可能是表示网络中节点重要性的有效候选者。本文的主要贡献是开发了一种方法，允许人们在研究特定感兴趣的网络时理解、比较和验证中心性指标。所提出的方法集成了以下步骤：选择感兴趣网络的中心性度量标准；对这些度量标准进行理论分类；通过主成分分析（PCA）确定感兴趣网络中的中心性潜在维度；验证所提出的中心性度量标准分类；并确定最能代表感兴趣网络的中心性度量标准。此外，我们还将所提出的方法应用于一个现有的感兴趣图，在我们的案例中是一个真实的学生友谊网络。我们选择了十八种在 SNA 中开发的、在特定库（CINNA）中可用并计算的中心性度量标准，对其进行了深入的定义，并提出了这些十八种度量标准的理论分类。PCA 显示了学生网络中六个中心性潜在维度的出现，并且大多数中心性指标在与理论分类中提出的类别相同的类别上达到饱和。此外，结果表明，与最常应用的指标相比，其他指标可能更适用于对学生友谊网络的研究。最后，我们提出的综合方法可以应用于其他中心性指标和/或其他类型的网络，而不仅仅是学生网络。
