We propose a new measure to quantify the impact of a node [Formula: see text] in controlling a directed network. This measure, called “control contribution” [Formula: see text], combines the probability for node [Formula: see text] to appear in a set of driver nodes and the probability for other nodes to be controlled by [Formula: see text]. To calculate [Formula: see text], we propose an optimization method based on random samples of minimum sets of drivers. Using real-world and synthetic networks, we find very broad distributions of [Formula: see text]. Ranking nodes according to their [Formula: see text] values allows us to identify the top driver nodes that can control most of the network. We show that this ranking is superior to rankings based on other control-based measures. We find that control contribution indeed contains new information that cannot be traced back to degree, control capacity or control range of a node.

中文翻译：

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控制贡献识别复杂网络中的顶级驱动节点

我们提出了一种新的方法来量化节点 [公式：见文本] 在控制有向网络中的影响。这种度量称为“控制贡献”[公式：见文本]，结合了节点[公式：见文本]出现在一组驱动节点中的概率和其他节点受[公式：见文本]控制的概率. 为了计算[公式：见正文]，我们提出了一种基于最小驱动程序集的随机样本的优化方法。使用现实世界和合成网络，我们发现 [公式：见文本] 的分布非常广泛。根据节点的 [公式：见文本] 值对节点进行排名，可以让我们确定可以控制大部分网络的顶级驱动节点。我们表明，该排名优于基于其他基于控制的措施的排名。