Minisymposium on “Networks, walks and matrix functions: new trends, results and potential issues”
July 17, 2019 at ICIAM in University of Valencia, Spain.
Talk given on joint work with Eric Horton (NC State); Blair Sullivan (NC State)
When one node surpasses another in centrality rankings as the underlying parameter varies, the nodes’ scores must cross at some parameter. Between such “collisions” the rankings remain stable, so the number of possible node-orderings for a centrality measure depends on the number of collisions. Analyzing the walk-classes of a graph reveals how often nodes can collide, ranking behavior at the parameter’s limits, and which nodes behave identically for a host of popular centralities.