The Exchange Gini Index "indicates the contribution to spatial focusing represented by the \(n(n-q)\) net interchanges in the system":
$$G^T_{RC, CR} = \frac{\sum_i \sum_{j \neq i} | M_{ij} - M_{ji} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}$$
This implementation solves the above formula by simply substracting the transposed matrix's values from the original one at one go.
Usage
migration.gini.exchange(m)
Arguments
m
migration matrix
Value
A number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.
References
David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. Demography34, 251--262