PureRank: A parameter-free recursive importance measure for network nodes

This study develops PureRank, a parameter-free importance measure for network nodes based on the recursive definition of importance (RDI). For every directed network, PureRank uniquely determines an importance score vector without user-specified parameters. PureRank can thus provide a neutral reference for parameter-dependent importance measures. PureRank is constructed in three steps: (i) nodes are classified into recurrent , transient , and dangling classes via strongly connected component decomposition; (ii) for each class, the local importance vector is obtained by choosing the parameters of the Katz equation on the class-restricted subnetwork according to the RDI principle; and (iii) the local importance vectors are aggregated into the PureRank vector. This modular design supports parallel and incremental computation while retaining a unified random-surfer interpretation. Numerical experiments on three SNAP networks show that PageRank has a computational advantage over PureRank except when the damping factor is close to one, and that the similarity of PageRank to PureRank depends on and the node classification. In the fully recurrent network, similarity increases monotonically with and reaches Kendall’s and Pearson correlation coefficient at , whereas in the two transient-dominated networks, similarity varies nonmonotonically with . PureRank is extended to multi-attribute networks. • PureRank is a parameter-free recursive importance measure for directed networks. • PureRank provides a neutral reference for parameter-dependent measures. • PureRank’s modular design enables parallel and incremental computation. • PureRank admits a random-surfer interpretation from a Markov chain perspective. • The splitting-network construction extends PureRank to multi-attribute networks.