單調性是公平衡量的一個吸引人的原則，它指出，隨著個人影響力的變化，這種衡量標準應該以平行的方式改變。 透過單調性，無論是在有向網絡還是無向網絡上，我們都公理化地表徵了兩個測度，即貝塔-測度和分數-測度。

Monotonicity is an appealing principle of fair measure which states that as individual influence change, the measure should change in parallel fashion. By means of monotonicity, we axiomatically characterize two measures, the beta-measure and the score-measure, whether on directed networks or undirected networks.

1 Introduction 3
2 Notation and Denitions 5
3 Monotonicity 7
4 Axiomatization of the beta-Measure and the Score-Measure 9
5 Results on Undirected Networks 15

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