Representation of the temporal ego-networks through graph evolution rules: a tool for Web3 applications

The understanding of how the complex systems governing various domains, from social interactions to financial transactions, is closely connected with our comprehension of their underlying dynamic networks and their evolution patterns. In particular, the evolution of these networks provides insights into the underlying mechanisms driving their changes, which can be pivotal for applications such as node segmentation, prediction of future states, and role discovery. Among the various approaches to studying network evolution, graph evolution rules (GERs) stand out since they produce human-readable outcomes without requiring any pre-assumptions about the underlying evolutionary mechanisms. In this work, we leverage GER to derive evolutionary node profiles (NEPs), capturing the distinct patterns of how nodes change over time within the network. These profiles allow us to identify groups of accounts characterized by similar evolution rules, revealing common interaction patterns. As a case study, we apply our approach to Sarafu, a complementary currency platform following the Web3 paradigm, which offers rich temporal economic data. Sarafu represents a contemporary human complex system that integrates humanitarian aid, collaboration, and financial aspects. By analyzing Sarafu’s network using our GER-based method, we identify two distinct evolutionary traits, uncovering significant behaviors that contribute to the platform’s operation. Our findings suggest the effectiveness of using graph evolution rules in real-world dynamic networks, showcasing their potential to enhance our understanding of the node-level dynamics of complex systems.