Fix GDC calculation in weighted networks

[Dimitris Kalamaras]

For instance, check this network:

0 0 0 1 0
1 0 0 0 0
0 1 0 0 0
0 0 0 0 1
0 0 0 0 0

It reports GDC = 0.009

But if we change a link weight ie.
0 0 0 1 0
1 0 0 0 0
0 1 0 0 0
0 0 0 0 12
0 0 0 0 0

then it reports GDC = 0.938 which is clearly wrong.

[Dimitris Kalamaras (dimitris-kalamaras)]

Will be using

( sum(maxDC-DC(v)) {for every v} ) / ( maxDC * (vertices-1) ) - verticesIsolated / vertices

as it is a variant of Freeman's formula, only with a different denominator.

[Dimitris Kalamaras (dimitris-kalamaras)]

The new formula for the second example yields GDC = 0.188.
For the same network where all edges are valued 10
0 0 0 12 0
12 0 0 0 0
0 12 0 0 0
0 0 0 0 12
0 0 0 0 0
it yields

GDC = 0.05

But it's no good when isolated vertices exist.

Perhaps, we should abandon the idea of GDC and offer just average DC and variance ...

[Dimitris Kalamaras (dimitris-kalamaras)]

SocNetV v1.5 and onwards will not compute GDC (or other group level centralization indices). It will advise the user to use variance or mean instead.