I am looking for description (name of algorithm, code, pseudocode, etc.) that can help me frame this problem and find the appropriate recursion and the most efficient solution.
Given a graph with weighted nodes and a starting node, I want to generate a weight-ordered list of nodes that are lying on a path that starts at the starting node and then proceeds by jumping to the next adjacent unvisited highest-value node, then to the next etc. until it can no longer continue (e.g. no adjacent nodes, no unvisited adjacent nodes, or all nodes were visited already once).
Am I correctly assuming that this is a variation on the traveling salesman problem? Any suggestions or pointers would be greatly appreciated. Algorithms just aren't my area of expertise...
Update from comments: This is not a homework question. ... There's actually years of empirical research behind simply being able to frame seemingly random mammalian behavior as an algorithmic problem. ... Without tackling these group dynamics algorithmically I will not be able to expand testing beyond my initial sample and unfortunately, regression analysis just won't do the trick.