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Zoo of Centralities: Encyclopedia of Node Metrics in Complex Networks

Sergey Shvydun

TL;DR

The Zoo of Centralities addresses the ill-posed and fragmented nature of node centrality by compiling a comprehensive encyclopedia of measures across diverse theoretical foundations.It provides a unified taxonomy, detailed descriptions, and an interactive online platform to enhance discoverability, benchmarking, and practical adoption of over 400 centrality metrics.The work integrates classical, modern, and hybrid metrics—from betweenness, closeness, and eigenvector-based measures to gravity, diffusion, entropy-based, and graphlet-based centralities—into a coherent reference for researchers and practitioners.By enabling standardized naming, cross-reference, and accessible implementations, the Centrality Zoo facilitates rigorous validation, comparison across networks, and informed selection of node metrics for tasks such as influence maximization, network dismantling, and diffusion analysis.

Abstract

Centrality is a fundamental concept in network science, providing critical insights into the structure and dynamics of complex systems such as social, transportation, biological and financial networks. Despite its extensive use, there is no universally accepted definition of centrality, leading to the development of a large variety of distinct centrality measures. These measures have grown so numerous that they resemble a 'zoo', each representing a unique approach to capturing node importance within a network. However, the increasing number of metrics being developed has led to several challenges, including issues of discoverability, redundancy, naming conflicts, validation and accessibility. This work aims to address these challenges by providing a comprehensive catalog of over 400 centrality measures, along with clear descriptions and references to original sources. While not exhaustive, this compilation represents the most extensive and systematic effort to date in organizing and presenting centrality measures. We also encourage readers to explore and contribute to the Centrality Zoo website at https://centralityzoo.github.io/, which provides an interactive platform for discovering and comparing centrality measures.

Zoo of Centralities: Encyclopedia of Node Metrics in Complex Networks

TL;DR

The Zoo of Centralities addresses the ill-posed and fragmented nature of node centrality by compiling a comprehensive encyclopedia of measures across diverse theoretical foundations.It provides a unified taxonomy, detailed descriptions, and an interactive online platform to enhance discoverability, benchmarking, and practical adoption of over 400 centrality metrics.The work integrates classical, modern, and hybrid metrics—from betweenness, closeness, and eigenvector-based measures to gravity, diffusion, entropy-based, and graphlet-based centralities—into a coherent reference for researchers and practitioners.By enabling standardized naming, cross-reference, and accessible implementations, the Centrality Zoo facilitates rigorous validation, comparison across networks, and informed selection of node metrics for tasks such as influence maximization, network dismantling, and diffusion analysis.

Abstract

Centrality is a fundamental concept in network science, providing critical insights into the structure and dynamics of complex systems such as social, transportation, biological and financial networks. Despite its extensive use, there is no universally accepted definition of centrality, leading to the development of a large variety of distinct centrality measures. These measures have grown so numerous that they resemble a 'zoo', each representing a unique approach to capturing node importance within a network. However, the increasing number of metrics being developed has led to several challenges, including issues of discoverability, redundancy, naming conflicts, validation and accessibility. This work aims to address these challenges by providing a comprehensive catalog of over 400 centrality measures, along with clear descriptions and references to original sources. While not exhaustive, this compilation represents the most extensive and systematic effort to date in organizing and presenting centrality measures. We also encourage readers to explore and contribute to the Centrality Zoo website at https://centralityzoo.github.io/, which provides an interactive platform for discovering and comparing centrality measures.

Paper Structure

This paper contains 431 sections, 664 equations, 3 figures, 1 table.

Table of Contents

  1. Centrality in Complex Networks
  2. Introduction
  3. Notation
  4. Classification of centrality measures
  5. Betweenness centrality measures
  6. Closeness centrality measures
  7. Path-based centrality measures
  8. Spectral centrality measures
  9. Random-walk-based centrality measures
  10. Local and semi-local centrality measures
  11. Community-based centrality measures
  12. Graphlet-based centrality measures
  13. Gravity-based centrality measures
  14. Vitality-based centrality measures
  15. Local dimension models
  16. ...and 416 more sections

Figures (3)

  • Figure 1: Zoo of Centralities.
  • Figure 2: Zachary’s karate club network Zachary1977.
  • Figure 3: Number of centrality measures proposed per year, showing an increasing trend over time. Source: Centiserver Mahdi2024 (data not updated after 2021).