Enumeration and properties of large discrete structures

这个项目的目的是研究随机图的一个基本性质，通过进一步发展一个最近引入的方法来枚举给定度的图的问题。使用这种新方法，该项目希望产生关于每个节点与随机图中其他节点的连接数量的新知识，并开发新的策略来计算具有给定属性的图或网络。该项目预计将产生新的理论成果，并增强数学研究的能力。通过使用这些理论组合对象来研究自然产生的网络，如社会网络、万维网网络和化合物，潜在的好处出现了。

This project aims to study a fundamental property of random graphs, by further developing a recently introduced approach to the problem of enumerating graphs with given degrees. Using this new method, the project expects to generate new knowledge on the number of connections that each node has with other nodes in a random graph, and to develop new strategies for counting the graphs or networks with a given property. The project expects to produce new theoretical results as well as enhanced capabilities of mathematical research. Potential benefits arise through the uses of these theoretical combinatorial objects to study naturally occurring networks such as social networks, the network of the world wide web, and chemical compounds.