Complex networks provide a flexible way to represent heterogeneous connectivity and interactions within real-world systems. Nowadays, people's lives are immersed in a world full of diverse and intricate complex networks. These networks not only provide conveniences that benefit our daily lives, such as enabling social networking, personalized recommendations, and shopping promotions. But they also bring certain negative impacts, such as facilitating the spread of misinformation, rumors, and infectious diseases. Therefore, developing a comprehensive understanding of the formation mechanisms, structures, and dynamics of complex networks in these socio-technical systems remains a pressing and challenging scientific endeavor. This thesis aims to explore multiple aspects of the applications of complex network analysis, with the following main contributions:

First, network dismantling. Network dismantling strategies will be critical for managing the spread of COVID-19. Public health interventions like social distancing and creating social bubbles aim to reduce infections by limiting interactions between social networks, thus reducing exposure risk. These measures essentially reconfigure the connections in the underlying contact networks. From a theoretical perspective, determining the optimal strategy to fragment networks to disrupt disease transmission maps to the optimal bond percolation (OBP) problem on networks. OBP involves selectively removing network connections to fragment the network into small components to minimize the size of the giant connected component. This has direct relevance for targeted social distancing policies that try to maximally disrupt the contact network with minimal disruption to individuals. In Chapter 4, I will formally introduce the OBP problem and discuss several heuristic strategies and benchmark algorithms.

Second, a reputation system based on a network/bipartite graph.
As online platforms like e-commerce, review sites, and social media grow, effectively evaluating quality and reputation through rating systems has become critical across many domains. Typically, an item's reputation is quantified by aggregating ratings and reviews left by users based on their experiences. However, user-contributed ratings can be intentionally misleading or biased, failing to reflect true underlying quality. In particular, certain users may exhibit consistent biases in their ratings across items, like being overly critical or lenient. Other users may be motivated to boost or attack specific targets. Such rating biases can significantly distort reputation systems and lead to poor recommendations if left unaccounted for. To address this challenge, evaluating the reputation of raters themselves becomes vital. We need scalable computational methods to infer which users provide accurate and reliable ratings versus those who skew ratings up or down. By correcting for rating biases, we can better reveal the intrinsic quality of items. In Chapter 5, we introduce an iterative balancing (IB) model that alternates between estimating user reputation and inferring unbiased item quality from the collective ratings. Experiments on movie rating data demonstrate the IB approach yields highly consistent results across iterations and effectively filters out different types of synthetic rating biases.

Third, information popularity prediction on social networks. The ability to predict the size of information cascades in online social networks is critical for a variety of applications, including decision-making and viral marketing. Traditional methods either rely on complex time-varying features, which are difficult to extract from multilingual and cross-platform content, or rely on network structures and properties, which are often difficult to obtain. To address these issues, we conducted an empirical study using data from two well-known social networking platforms (WeChat and Weibo). The findings suggest that the information cascade process is best described as an activation-decay dynamic. Based on this, we develop an Activate-Decay (AD)-based algorithm that can accurately predict the long-term popularity of online content based only on the number of early retweets. An indirect relationship between the peak retweeting amount and the total propagation amount was also found. Finding the peak of information diffusion can significantly improve the prediction accuracy of the model. This content will be introduced in detail in Chapter 6.

The research presented in this thesis provides valuable insights into the function and influence of complex networks across various real-world systems.