At Salesforce, one of the ways we measured influence was by the amount of internal social network activity an individual accumulated... posts, likes, replies, etc. In nearly all cases, the higher ups had the most influence.
everything you make an input of the recognition process become an output of the office politics hack. obviously it corelates. at my company, were its not part of recognition, higher ups have zero posts on the information sharing systems.
Hard to define, do you have ideas :)
In my experience influence is earned using much of what you outline. Lovely blog post.
The most succinct thing I've come up with is: "You're an influential engineer if an engineer magically becomes better just by sitting next to you."