# Centrality Measures in Networks

arXiv: https://arxiv.org/abs/1608.05845 · HTML: https://mlsanity.com/paper/1608.05845/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2016.

## Built on by (most cited first, 11 of 11)

- [Social Diversity Reduces the Complexity and Cost of Fostering Fairness](https://mlsanity.com/paper/2211.10517/) (2022)
- [NAZM: Network Analysis of Zonal Metrics in Persian Poetic Tradition](https://mlsanity.com/paper/2505.08052/) (2025)
- [Centrality-Based Node Feature Augmentation for Robust Network Alignment](https://mlsanity.com/paper/2304.12751/) (2023)
- [Centrality-Based Pruning for Efficient Echo State Networks](https://mlsanity.com/paper/2603.20684/) (2026)
- [Opinion Leader Detection in Online Social Networks Based on Output and Input Links](https://mlsanity.com/paper/2208.13161/) (2022)
- [Fixed-Point Centrality for Networks](https://mlsanity.com/paper/2209.07070/) (2022)
- [Analyzing Key Users' behavior trends in Volunteer-Based Networks](https://mlsanity.com/paper/2310.05978/) (2023)
- [A multi-core periphery perspective: Ranking via relative centrality](https://mlsanity.com/paper/2406.04487/) (2024)
- [From Federated Learning to X-Learning: Breaking the Barriers of Decentrality Through Random Walks](https://mlsanity.com/paper/2509.03709/) (2025)
- [Sensor Placement for Urban Traffic Interpolation: A Data-Driven Evaluation to Inform Policy](https://mlsanity.com/paper/2601.10747/) (2026)
- [Rethinking Reservoir Pruning: A Dynamical Perspective for Echo State Networks](https://mlsanity.com/paper/2608.04593/) (2026)

## Abstract (arXiv)

We show that prominent centrality measures in network analysis are all based on additively separable and linear treatments of statistics that capture a node's position in the network. This enables us to provide a taxonomy of centrality measures that distills them to varying on two dimensions: (i) which information they make use of about nodes' positions, and (ii) how that information is weighted as a function of distance from the node in question. The three sorts of information about nodes' positions that are usually used -- which we refer to as "nodal statistics" -- are the paths from a given node to other nodes, the walks from a given node to other nodes, and the geodesics between other nodes that include a given node. Using such statistics on nodes' positions, we also characterize the types of trees such that centrality measures all agree, and we also discuss the properties that identify some path-based centrality measures.