论文标题
基于当前流量的网络中心性可调节范围
Adjustable reach in a network centrality based on current flows
论文作者
论文摘要
量化单个节点的“重要性”的中心性是现代网络理论中最重要的概念之一。最突出的中心度度量可以表示为对节点对之间影响流的聚集。由于可以定义影响的许多方式，因此正在使用许多不同的集中度措施。参数化的中心可以通过调整最适合给定网络的制度的中心度计算来进一步的灵活性和实用性。在这里，我们确定了两类中心性参数。到达参数控制远处节点之间影响流的衰减。 Grasp参数控制着中心性在多个，通常是非对地的路径上发送影响流的潜力。将这些类别与Borgatti的中心性类型相结合[S. P. Borgatti，社交网络27，55-71（2005）]，我们到达了一个新颖的参数化中心分类系统。使用此分类，我们确定了明显的缺乏径向，达到参数化并基于无环的，保守的影响流的任何中心度度量。因此，我们引入了地面中心性，这是确切的这种类型的量度。由于其在分类法中的独特地位，地面式中心性比类似的中心具有显着优势。我们证明，与其他保守流中心相比，它具有更简单的数学描述。与其他到达中心相比，它坚定地保留了各种网络体系结构的直观等级顺序。我们还表明，它在节点之间产生了中心价值的一致分布，既不相等扩散（DeLocalization），也不过分集中于一些节点（本地化）。其他到达中心分别在常规网络和集线器网络上表现出这两种行为。
Centrality, which quantifies the "importance" of individual nodes, is among the most essential concepts in modern network theory. Most prominent centrality measures can be expressed as an aggregation of influence flows between pairs of nodes. As there are many ways in which influence can be defined, many different centrality measures are in use. Parametrized centralities allow further flexibility and utility by tuning the centrality calculation to the regime most appropriate for a given network. Here, we identify two categories of centrality parameters. Reach parameters control the attenuation of influence flows between distant nodes. Grasp parameters control the centrality's potential to send influence flows along multiple, often nongeodesic paths. Combining these categories with Borgatti's centrality types [S. P. Borgatti, Social Networks 27, 55-71 (2005)], we arrive at a novel classification system for parametrized centralities. Using this classification, we identify the notable absence of any centrality measures that are radial, reach parametrized, and based on acyclic, conservative flows of influence. We therefore introduce the ground-current centrality, which is a measure of precisely this type. Because of its unique position in the taxonomy, the ground-current centrality has significant advantages over similar centralities. We demonstrate that, compared to other conserved-flow centralities, it has a simpler mathematical description. Compared to other reach centralities, it robustly preserves an intuitive rank ordering across a wide range of network architectures. We also show that it produces a consistent distribution of centrality values among the nodes, neither trivially equally spread (delocalization), nor overly focused on a few nodes (localization). Other reach centralities exhibit both of these behaviors on regular networks and hub networks, respectively.
