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