A Graph-Theoretical Analysis of the Lightning Network

The Lightning Network is the most adopted layer-2 solution for Bitcoin, shifting many transactions off-chain through bidirectional channels to improve scalability and reduce costs. Despite its growing usage, few studies have been conducted to investigate its structure and how it evolved over time. In this work, we analyze the structural properties of the public Lightning Network using graph theory, collecting both real-time and historical data. We have then considered multiple filtering strategies to isolate different parts of the network, such as excluding single-connection nodes or central hubs. The results show that as the network has grown, its average connectivity has decreased, and its reliance on hubs has increased. This structure enables efficient routing, but also conceals some issues concerning the network resilience in case of hub failures.