Hypergraph models for complex discrete systems

该项目旨在更好地了解各种超大型超图的结构和性质。超图是非常通用的数学对象，可用于对复杂的离散系统进行建模。它们自然地出现在许多领域，如生态学、化学和计算机科学。尽管如此，我们对非常大的或随机的超图的理论理解远远落后于深入研究的图的特殊情况。这个项目将回答许多关于大型随机超图的基本问题。该项目的预期成果还包括用于处理超图的新工具，例如用于采样超图的高效算法。这些结果将使在工作中使用超图的研究人员受益，并将提高澳大利亚在这一领域研究的声誉。

This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This project will answer many fundamental questions about large, random hypergraphs. The expected outcomes of the project also include new tools for working with hypergraphs, such as efficient algorithms for sampling hypergraphs. These outcomes will benefit researchers who use hypergraphs in their work and will enhance Australia's reputation for research in this area.