# Exchange Gini Index

### Description

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{∑_i ∑_{j \neq i} | M_{ij} - M_{ji} | }{
(2n(n-1)-1) ∑_i ∑_{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

1 |

### 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.

*Demography***34**, 251–262

### See Also

`migration.gini`

`migration.gini.exchange.standardized`

### Examples

1 2 3 | ```
data(migration.hyp)
migration.gini.exchange(migration.hyp) # 0.05555556
migration.gini.exchange(migration.hyp2) # 0.04166667
``` |

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