We propose to use eigenvector centrality (EVC) as the basis for determining stable paths and arrive at benchmarks for the number of path transitions incurred with stability-based routing in cognitive radio ad hoc networks (CRAHNs) wherein secondary users (SUs) use the available (idle) licensed channels of primary users (PUs). We model a time-variant network graph (at any time instant) of SU nodes whose adjacency matrix indicates the number of common available PU channels in the mutually intersecting neighbourhoods of any two SU nodes at the time instant. Such an adjacency matrix is used as the basis to compute the EVC of the vertices in the network graph of SU nodes and determine an end-to-end source-destination path whose constituent SU nodes have a higher EVC. Simulation results indicate EVC-based paths between any two SU nodes incur significantly fewer transitions without any appreciable increase in the average hop count per path.