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.