This thesis explores two central themes, each contributing to a better understanding of complex network dynamics and the challenges they present. Firstly, in Theme 1, a dynamic model for social network segregation is presented, based on a graph cut metric. By incorporating social context and analyzing historical patterns, the thesis aims to better comprehend network segregation, as seen during political elections where people often form groups based on their political preferences. A Hidden Markov bridge estimator of social network segregation is proposed to capture long-range dependencies, outperforming existing Hidden Markov estimators that do not take social context into account. Additionally, an algorithmic recommendation algorithm is presented to use exogenous incentives to regulate segregation in online social network platforms. The thesis also extends the concept of segregation to the glass ceiling effect in social networks, proposing a mutual information-based measurement, that quantifies the effect as the information gained from nodes' demographic information over mutual information that only accounts for node degrees. This metric is shown to be more comprehensive than degree assortativity and homophily in describing the glass ceiling effect in citation networks. Secondly, Theme 2 focuses on designing and analyzing Blockchain-based Online Social Networks (BOSNs) that prevent or mitigate threats such as echo chambers and misinformation placed by segregation in Theme 1. Due to the decentralized nature of blockchain systems, which do not rely on a single proprietary authority to manage data, BOSNs are immune to misinformation. The thesis evaluates the effectiveness of BOSNs by simulating the spread of misinformation using a SIR model and estimates parameters from actual Twitter data. The real-world blockchain-based cryptocurrency market is also analyzed, with a focus on the use of multi-variate Hawkes process to model block arrivals in the bitcoin blockchain. Finally, a graph-based approach is presented to identify suspicious blockchain transactions using conformal prediction combined with the edge exchangeable model, resulting in a conformal detector that guarantees a low false positive rate. Overall, this thesis provides insights into complex network dynamics and their implications in both social and financial contexts, with practical applications in designing more trustworthy and resilient social networks.