The Invisible Internet Project (I2P) is a decentralized peer-to-peer anonymity network that protects users’ privacy by routing traffic through encrypted tunnels across volunteer-run routers (nodes). Its distributed nature raises critical questions about structural resilience, specifically, how well it can withstand random (stochastic) failures and targeted (adversarial) attacks. This study models I2P’s overlay using three representative network graphs or topologies: Random Graph (RG), Scale-Free (SF), and a theoretical modeling of I2P’s network, herein referred to as I2P Prime (I2P’), all experimented with 50,000 nodes (peers) each to reflect the real-world conditions of the I2P network. Simulations under random node removals show that all three networks retain large connected components (LCC) beyond 50% node loss, with I2P Prime maintaining superior efficiency. However, targeted attacks based on degree or betweenness centrality reveal substantial vulnerabilities. The SF network model of I2P collapsed rapidly, often below 30% node removal due to its hub-centric design. In contrast, I2P Prime exhibits stronger fault tolerance, requiring nearly 50% of critical nodes to be removed before global connectivity fails. These findings underscore the structural advantages of topologies like I2P Prime, which combines distributed connectivity and resilience to percolation and Perturbation. For developers, enhanced adaptive peer selection and dynamic routing mechanisms could enhance robustness without undermining anonymity. For policymakers, our results highlight how targeted interventions might fragment illicit activity with minimal collateral impact. This work provides actionable insights into designing resilient anonymity networks that preserve privacy under stochastic and adversarial attacks.