Some examples of very optimized pathfinding can be found in the node A Better Word Morph Builder. I think that the general idea for solving your problem is giving each machine an unique number (which is already done if the network map is implemented as you described), buiding a datastructure like 
%network_map = (
12567 =>            # the machine id
[335, 456, 338],    # the id's of machines it is directly connected to
335 => [12657, 558, 667, 333]
# etc
)

[download]
and browsing this datastructure with some tree search algorithm. I myself prefer bidirectional search, the working example is given e.q. in this node, but i think that your network is small enough for using the breadth-first search without any significant performance loss.

Sorry for my English :)

     s;;Just-me-not-h-Ni-m-P-Ni-lm-I-ar-O-Ni;;tr?IerONim-?HAcker ?d;print

In reply to Re: Finding a Path by Ieronim
in thread Develop a Tree by Herkum

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