具有高阶结构的图的混合模式
Mixing patterns in graphs with higher-order structure
摘要：
在本文中，我们研究了具有非平凡聚类和基于子图的非平凡混合（基于子图联合度的顶点连接到其他顶点的趋势）的高阶网络的渗流性质。我们的分析方法是基于生成函数。我们还提出了一个蒙特卡罗图生成算法，以绘制随机网络的合奏图与固定的统计。我们使用我们的模型来理解网络微观结构的影响，通过安排集群，对全局属性。最后，我们使用一个边不相交的团覆盖来表示经验网络使用我们的配方，发现由此产生的模型提供了一个显着的改进，基于边的理论。
英文摘要：
In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our analytical method is based on generating functions. We also propose a Monte Carlo graph generation algorithm to draw random networks from the ensemble of graphs with fixed statistics. We use our model to understand the effect that network microstructure has, through the arrangement of clustering, on the global properties. Finally, we use an edge disjoint clique cover to represent empirical networks using our formulation, finding the resultant model offers a significant improvement over edge-based theory.
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