Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2501.00417 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909018485686272 |
|---|---|
| author | Masuyama, Hiroyuki |
| author_facet | Masuyama, Hiroyuki |
| contents | 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 interpretation. Numerical experiments on three SNAP networks show that PageRank has a computational advantage over PureRank except when the damping factor $d$ is close to one, and that the similarity of PageRank to PureRank depends on $d$ and the node classification. In the fully recurrent network, similarity increases monotonically with $d$ and reaches Kendall's $τ_b=0.966$ and Pearson correlation coefficient $=1.000$ at $d=0.999$, whereas in the two transient-dominated networks, similarity varies nonmonotonically with $d$. PureRank is extended to multi-attribute networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00417 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | PureRank: A parameter-free recursive importance measure for network nodes Masuyama, Hiroyuki Social and Information Networks 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 interpretation. Numerical experiments on three SNAP networks show that PageRank has a computational advantage over PureRank except when the damping factor $d$ is close to one, and that the similarity of PageRank to PureRank depends on $d$ and the node classification. In the fully recurrent network, similarity increases monotonically with $d$ and reaches Kendall's $τ_b=0.966$ and Pearson correlation coefficient $=1.000$ at $d=0.999$, whereas in the two transient-dominated networks, similarity varies nonmonotonically with $d$. PureRank is extended to multi-attribute networks. |
| title | PureRank: A parameter-free recursive importance measure for network nodes |
| topic | Social and Information Networks |
| url | https://arxiv.org/abs/2501.00417 |