This repository provides a collection of normalized network centralization measures implemented in R along with analysis scripts for evaluating and visualizing their behavior on canonical and perturbed graph families.
The work is based on the formal definitions from the network science literature and implements the measures in a way that is consistent with axiomatic foundations and theoretical boundary conditions. All scripts rely on the igraph package for network modeling and ggplot2 / dplyr for visualization and data handling.
Core implementation of normalized network centralization measures:
- ABH: Assortativity-Based Hubness
- ECD: Eigenvector Centrality Dispersion
- NBC: Normalized Betweenness Centralization
- NCC: Normalized Closeness Centralization
- NDC: Normalized Degree Centralization
- NDE: Normalized Degree Entropy
- NDV: Normalized Degree Variance
- NGC: Normalized Gini Coefficient
- NHD: Normalized Degree Hubness
- NHT: Normalized Hub Formation Tendency
- NNC: Normalized Natural Connectivity
This script can be sourced directly into an R session and applied to any igraph object.
Analysis of centralization measures on canonical graph families:
- Star graphs
- Ring graphs
- Complete graphs
The script evaluates all measures for graphs of various sizes and exports the results as PDF plots (centralization_analysis.pdf).
Analysis of centralization measures on perturbed graphs, where a single edge is rewired in star, ring, and complete graphs.
The script evaluates the measures for graphs of various sizes and exports the results as PDF plots (centralization_analysis_perturbed.pdf).
- Clone the repository and open it in R.
- Install required packages if not already installed:
install.packages(c("igraph", "ggplot2", "dplyr"))
- Source the core functions: source("centralization_measures.R")
- Run one of the analysis scripts:
source("centralization_analysis.R") source("centralization_analysis_perturbed.R") - Plots will be generated as PDF files in the working directory.
If you use these implementations or analyses, please cite:
Saberi M, Samin A. (2025). Evaluating global measures of network centralization: axiomatic and numerical assessments.