Percolation theory investigates systems of interconnected units, their resilience to damage and their propensity to propagation. For random networks we can solve the percolation problems analytically using the generating function formalism. Yet, with the introduction of higher order networks, the generating function calculations are becoming difficult to perform and harder to validate. Here, I illustrate the mapping of percolation in higher order networks to percolation in chygraphs. Chygraphs are defined as a set of complexes where complexes are hypergraphs with vertex sets in the set of complexes. In a previous work I reported the generating function formalism to percolation in chygraphs and obtained an analytical equation for the order parameter. Taking advantage of this result, I recapitulate analytical results for percolation problems in higher order networks and report extensions to more complex scenarios using symbolic calculations. The code for symbolic calculations can be found at https://github.com/av2atgh/chygraph.

翻译：渗流理论研究相互连接单元系统的抗损伤能力及其传播倾向。对于随机网络，我们可利用生成函数形式化方法解析求解渗流问题。然而随着高阶网络的出现，生成函数计算变得难以执行且更难验证。本文阐述了将高阶网络渗流映射为chygraph渗流的方法。Chygraph定义为复合体集合，其中复合体是以复合体集合中的顶点集为顶点集的超图。在先前工作中，我报告了chygraph渗流的生成函数形式化方法，并得到了序参量的解析方程。利用这一成果，我重新推导了高阶网络渗流问题的解析结果，并报告了通过符号计算扩展到更复杂场景的进展。符号计算代码可在https://github.com/av2atgh/chygraph获取。