Matrix plots of reordered bistochastized transaction flow tables: A United States intercounty migration example

TL;DR

This paper visualizes U.S. intercounty migration data using matrix plots with various reorderings, revealing regional migration patterns and hub-like structures, and introduces methods applicable to other transaction flow datasets.

Contribution

It introduces matrix plot visualization techniques based on eigenvector and hierarchical clustering orderings for bistochasticized flow tables, highlighting regional migration features.

Findings

Distinct migration patterns between Sunbelt and Black Belt counties

Identification of hub-like, cosmopolitan and provincial regions

Methodology applicable to other transaction flow data

Abstract

We present a number of variously rearranged matrix plots of the $3, 107 \times 3, 107$ 1995-2000 (asymmetric) intercounty migration table for the United States, principally in its bistochasticized form (all 3,107 row and column sums iteratively proportionally fitted to equal 1). In one set of plots, the counties are seriated on the bases of the subdominant (left and right) eigenvectors of the bistochastic matrix. In another set, we use the ordering of counties in the dendrogram generated by the associated strong component hierarchical clustering. Interesting, diverse features of U. S. intercounty migration emerge--such as a contrast in centralized, hub-like (cosmopolitan/provincial) properties between cosmopolitan "Sunbelt" and provincial "Black Belt" counties. The methodologies employed should also be insightful for the many other diverse forms of interesting transaction flow-type data--interjournal citations being an obvious, much-studied example, where one might expect that the journals Science, Nature and PNAS would display "cosmopolitan" characteristics.