Path plant network
We employ our customized algorithm using graphsp_IP_res.m to grow a
resistive path network with 
nodes. We set 
and choose the state
weight that penalizes the mean-square deviation from the network average,
.
As shown below, for 
, we obtain a centralized controller that
requires information exchange between all nodes. As 
increases, the
number of added edges gradually decreases. Finally, for 
, a single edge is added and this edge generates the longest
cycle. This is in agreement with recent theoretical developments of
Zelazo, Schuler, and
Allgower ’13 where it was shown that the longest cycle is most beneficial
for improving the 
performance of tree networks.
Blue lines identify edges in the plant graph; red lines identify edges in
the controller graph; 
identifies the value of the
regularization parameter for which all edge weights in the
controller graph are equal to zero.
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