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

TL;DR
PureRank is a parameter-free, recursive importance measure for network nodes that offers a neutral alternative to parameter-dependent measures like PageRank, with efficient computation and broad applicability.
Contribution
The paper introduces PureRank, a novel parameter-free importance measure based on recursive importance definition, applicable to directed networks and extendable to multi-attribute networks.
Findings
PureRank provides a unique importance score without user-defined parameters.
PageRank is computationally faster than PureRank except near damping factor d=1.
Similarity between PageRank and PureRank depends on the damping factor and network structure.
Abstract
This study develops PureRank, a parameter-free importance measure for network nodes based on the recursive definition of importance (RDI). For any 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 {\it recurrent}, {\it transient}, and {\it 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…
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