# On the limiting behavior of parameter-dependent network centrality measures

arXiv: https://arxiv.org/abs/1312.6722 · HTML: https://mlsanity.com/paper/1312.6722/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2013.

## Built on by (most cited first, 2 of 2)

- [Efficient Algorithms for Computing Random Walk Centrality](https://mlsanity.com/paper/2510.20604/) (2025)
- [Gaussian Relational Graph Transformer](https://mlsanity.com/paper/2605.15575/) (2026)

## Abstract (arXiv)

We consider a broad class of walk-based, parameterized node centrality measures for network analysis. These measures are expressed in terms of functions of the adjacency matrix and generalize various well-known centrality indices, including Katz and subgraph centrality. We show that the parameter can be "tuned" to interpolate between degree and eigenvector centrality, which appear as limiting cases. Our analysis helps explain certain correlations often observed between the rankings obtained using different centrality measures, and provides some guidance for the tuning of parameters. We also highlight the roles played by the spectral gap of the adjacency matrix and by the number of triangles in the network. Our analysis covers both undirected and directed networks, including weighted ones. A brief discussion of PageRank is also given.