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<<<-------- Edmund Chattoe-Brown-------->>>
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> Dear All,
> I am trying to construct (by simulation) a network with a given
> percentage of two way ties (the rest one way). Each social actor has a
> limit on the number of ties they can support. (Call this "capacity".)
> The programme works by doing all the two way ties first and then
> "filling up" any unused capacity with one way ties.
Are the capacities equal for all nodes?
Are the capacities just upper bounds or they have to be realized
by a constructed graph?
I think you have to distinguish between input and output capacities.
Your problem can be related to "graphic(al) sequences"
You can also consider the idea of generating some graph (may be
with multiple links and loops) that realizes your conditions
(look at the approach used for preferential attachment in
and correct it afterward using the Z2И transformation:
u--v u v
/ ---> | /|
/ |/ |
w--t w t
(u:v), (v:w), (w:t)
(u:w), (v:w), (v:t)
(see the rule P3 on page 3 in
adapted for directed graphs and loops (you get a set of possible
transformations, you can also impose some restrictions such us
(u:w) is not a link). These transformations preserve the degrees of
nodes and the graph connectivity.
Vladimir Batagelj, University of Ljubljana, FMF, Department of Mathematics
Jadranska 19, 1000 Ljubljana, Slovenia
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