Abstract
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.
Highlights
Migration and remittances have become important facets of modern human society
We present a modification to barcodes, the output diagram of persistent homology, by introducing a coloring scheme that distinguishes features of the same dimension
3 Methods 3.1 Directed clique complexes The central idea is the following: given a directed network, construct a mathematical object C in such a way that resulting topological features of C correspond to patterns in the network. One advantage of this approach is that these patterns, which give a higher-order description of the underlying network, can be extracted via their corresponding topological features using tools from algebraic topology
Summary
The United Nations’ Department of Economics and Social Affairs (UNDESA) reports that the total number of international migrants, defined as foreign-born or foreign citizens for the purpose of estimation, has continued to grow rapidly from year 2000 to year 2015 at a rate faster than that of the world’s population. Many published reports, such as UNDESA’s [1] and World Bank’s [2], provide comprehensive statistical descriptions and forecasts on world migration and remittances. These measure the diaspora and reach of migrants (2019) 8:1
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