Yulia Gel, On the the Role of Higher Order Topological Properties in Functionality of Complex Networks

The emerging machinery of topological data analysis and, particularly, persistent homology allow to unveil some critical characteristics behind organization of complex networks and interactions of their components at multi-scale levels, which are otherwise largely inaccessible with conventional analytical approaches.

The ultimate idea is to study properties of progressively finer simplical complexes on graphs over a range of (dis)similarity thresholds and then to assess which topological characteristics exhibit a longer lifespan (or persist) across multiple (dis)similarity thresholds. Such persistent features are likelier to be related to intrinsic network organization and functionality.

In turn, features with shorter lifespan can be referred to as topological noise. In this talk we discuss how geometry and topology of blockchain transaction networks, assessed with the machinery of persistent homology, can enhance our understanding of hidden mechanisms behind blockchain graph anomalies and associated crypto price dynamics.