What's the reasoning for safety wire on aircraft, and the reasoning behind the way it's routed? I'm assuming saftey wire is used near propeller assemblies where a lot of vibration occurs, or where the different speeds and altitudes aircraft are at could cause expansion or contraction based on temperature.  Is that correct? 

I'm also wondering the reasoning for routing them in this manner. Is it done this way to counter vibration so both bolts don't loosen? If one is going counter-clockwise due to vibration, I'm assuming it'd be tightening the other bolt or vice versa?
Safety wire (positive wire locking) is done in areas where there is a possibility of the bolt getting loose due to vibration (also in other critical areas); this is done in a way such that the loosening of the bolt is counteracted by the tension in the wire i.e. in case the bolts loosen, the locking wire becomes taut and prevents further movement of the bolt.



safety wire examples; image from www.stangtv.com

There are different ways of doing wire locking for locking depending on the number of fasteners involved, but the basics are the same.



Safety wires; image from FAA AC 43.13-1B - Acceptable Methods, Techniques, and Practices - Aircraft Inspection and Repair