在信息科技快速发展的背景下，作为基础支撑学科的离散数学成为现代数学发展最为迅速和最为活跃的领域。图论作为离散数学的重要分支，是刻画离散对象以及他们之间的相互关系的理想数学模型，是复杂网络的基本载体。.本项目以图理论为基础，针对复杂网络的异质性、时变性等特征，运用符号图、超图、正则引理、子图存在性等理论，从以下几个方面展开研究：首先，提出高维异质网络的结构分析和预测算法，包括符号网络的社团划分和时序网络的链路预测问题；其次，开展异质网络的局部子图研究，涉及时序网络和符号网络的高阶子图挖掘和分解算法；最后，探索正则引理在复杂网络社团划分或数据聚类中的应用，为社团个数的确定、聚类算法的设计提供理论支持。.本项目既重视图基础理论研究，也重视实际问题驱动的图与网络算法设计和模型建立，为图论方法在网络科学中的进一步推广提供一定的模型和算法基础。

Under the background of the rapid development of information technology, discrete mathematics, as the essential supporting discipline, has become the most rapidly developing and active field of modern mathematics. Graph theory, as a critical branch of discrete mathematics, is an ideal mathematical model to describe discrete objects and their relations and is the primary carrier of complex networks. .Based on graph theory, aiming at the heterogeneity and temporality of complex networks, this project applies the theories of signed graphs, hypergraphs, regular lemma, subgraph existence to conduct research from the following perspectives. Firstly, the structural analysis and prediction algorithms of high-dimensional heterogeneous networks are proposed, including community detection of signed networks and link prediction of temporal networks. Secondly, the local subgraph of heterogeneous systems is studied, which involves the mining and decomposition of higher-order subgraphs of temporal and signed networks. Finally, explore the application of regularity lemma in complex networks to provide theoretical support for the determination of the number of communities and the design of clustering algorithms. .This project not only pays attention to the graph theory research, but also focuses on the design and modeling of the graph and network algorithm driven by practical problems. It will provide a certain model and algorithm basis for the further promotion of graph methods in network science.