Measures of centrality in networks defined by means of matrix algebra, like PageRank-type centralities, have been used for over 70 years. Recently, new extensions of PageRank have been formulated and may include a personalization (or teleportation) vector. It is accepted that one of the key issues for any centrality measure formulation is to what extent someone can control its variability. In this paper, we compare the limits of variability of two centrality measures for complex networks that we call classic PageRank (PR) and biplex approach PageRank (BPR). Both centrality measures depend on the so-called damping parameterα that controls the quantity of teleportation. Our first result is that the intersection of the intervals of variation of both centrality measures is always a nonempty set. Our second result is that when α is lower that 0.48 (and, therefore, the ranking is highly affected by teleportation effects) then the upper limits of PR are more controllable than the upper limits of BPR; on the contrary, when α is greater than 0.5 (and we recall that the usual PageRank algorithm uses the value 0.85), then the upper limits of PR are less controllable than the upper limits of BPR, provided certain mild assumptions on the local structure of the graph. Regarding the lower limits of variability, we give a result for small values of α. We illustrate the results with some analytical networks and also with a real Facebook network.

中文翻译：

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个性化PageRank的参数可控性：经典模型与双工方法。

通过矩阵代数定义的网络中的中心度（例如PageRank型中心度）已使用了70多年。最近，已经制定了PageRank的新扩展，其中可能包括个性化（或传送）矢量。人们公认，任何集中度度量公式化的关键问题之一是人们可以在多大程度上控制其可变性。在本文中，我们比较了两种复杂性网络的中心度度量的可变性极限，我们将其称为经典PageRank（PR）和双工方法PageRank（BPR）。两种集中度度量都取决于控制阻尼量的所谓阻尼参数α。我们的第一个结果是两个中心性度量的变化间隔的交集始终是一个非空集。我们的第二个结果是，当α小于0.48时（并且，因此，排名受传送效应的影响很大），那么PR的上限比BPR的上限更容易控制。相反，当α大于0.5（并且我们回想起通常的PageRank算法使用值0.85）时，如果对BPR的局部结构做出某些温和的假设，则PR的上限比BPR的上限更难控制。图。关于变异性的下限，我们给出了一个小的α值的结果。我们用一些分析网络和一个真实的Facebook网络来说明结果。则只要对图的局部结构有某些温和的假设，PR的上限就不如BPR的上限可控制。关于变异性的下限，我们给出了一个小的α值的结果。我们用一些分析网络和一个真实的Facebook网络来说明结果。则只要对图的局部结构有某些温和的假设，PR的上限就不如BPR的上限可控制。关于变异性的下限，我们给出了一个小的α值的结果。我们用一些分析网络和一个真实的Facebook网络来说明结果。