As an abstract representation of ubiquitous interactions, complex networks ignore the individual differences between homogeneous objects and focus on their interactions and the resulting systems with complex behavioral patterns and intelligence beyond the individual, leading to an understanding of the complexity that cannot be captured at the individual level. By its very nature, a complex network is a new research paradigm based on evolutionary philosophy.
In the formation of the network, heterogeneity, as an important feature, shapes the overall appearance of the network, that is to say, a small number of components can always be found in the network, and they exert a powerful influence on the structure and function of the network far beyond the vast majority of individuals. With the rapid growth of the network size, how to capture the key minority of the network has become an increasingly important issue. This thesis takes information mining on complex networks as the theme, from the perspective of statistical physics, around the core scientific issue of node identification, has launched a full-spectrum exploration of related centrality indices, important microstructures, network dynamics, performance evaluation criteria, clique structural identification, etc. Specifically, in Chapter 1, we introduce the background of this research and the scientific issues involved. In Chapter 2, we introduce important preliminaries that are necessary to understand this research. In Chapter 3, we introduce the topic of node identification, review the relevant research literature, and introduce common performance evaluation criteria. In Chapter 4, we propose and prove the DHC theorem on directed weighted networks and apply it to the analysis of World Trade Web and the quantification of the trade influence of countries or regions. In Chapter 5, we discuss the importance of the cycle structure to the network, and propose a cycle-based analysis framework, including cycle representation, node centralities, spreading model and a controllability evaluation criterion of centrality index. In Chapter 6, we discover and prove a network convergence theorem that maximizes the spreading influence of nodes and also measures the influence of nodes within a given explicit range. In Chapter 7, we propose a fast exact algorithm for maximum clique search in large-scale networks. Besides being very efficient, it also shows that the solution complexity of the maximum clique is approximately independent of the size of the network. Finally, in Chapter 8, we conclude the full text and discuss future work.