Tracing patterns and shapes in remittance and migration networks via persistent homology

Pattern detection in network models provides insights to both global structure and local node interactions. In particular, studying patterns embedded within remittance and migration flow networks can be useful in understanding economic and sociologic trends and phenomena and their implications both in regional and global settings. We illustrate how topo-algebraic methods can be used to detect both local and global patterns that highlight simultaneous interactions among multiple nodes, giving a more holistic perspective on the network fabric and a higher order description of the overall flow structure of directed networks. Using the 2015 Asian net migration and remittance networks, we build and study the associated directed clique complexes whose topological features correspond to specific flow patterns in the networks. We generate diagrams recording the presence, persistence, and perpetuity of patterns and show how these diagrams can be used to make inferences about the characteristics of migrant movement patterns and remittance flows.