标题： 有向图中非正则性与营养级一致性的关系 显示英文标题

标题： The connection between non-normality and trophic coherence in directed graphs

摘要： 营养层次一致性和非正规性都是描述有向图或网络整体方向性的方法。 营养层次一致性可以看作是衡量图能被分成不同层的清晰程度的指标，而非正规性则是衡量矩阵与其转置不相似的程度的指标。 我们首先通过考虑文献中存在的联系，并计算一些玩具网络的营养层次一致性和非正规性，来探索营养层次一致性与非正规性之间的关系。 然后我们探讨在SIS模型中流行病的持续性如何依赖于一致性，并且这如何与非正规性相关联。 由线性算子支配的动力学中的类似效应表明，将营养层次一致性的概念扩展到不一定表示图的矩阵可能是有用的。 显示英文摘要

摘要： Trophic coherence and non-normality are both ways of describing the overall directionality of directed graphs, or networks. Trophic coherence can be regarded as a measure of how neatly a graph can be divided into distinct layers, whereas non-normality is a measure of how unlike a matrix is with its transpose. We explore the relationship between trophic coherence and non-normality by first considering the connections that exist in the literature and calculating the trophic coherence and non-normality for some toy networks. We then explore how persistence of an epidemic in an SIS model depends on coherence, and how this relates to the non-normality. A similar effect on dynamics governed by a linear operator suggests that it may be useful to extend the concept of trophic coherence to matrices which do not necessarily represent graphs.