The core of this analysis is the distinction() function, which calculates the distinction centrality score for nodes in an igraph object.
To use the distinction function in your own R project, you can download the script or source it directly from GitHub:
# Load igraph
library(igraph)
library(DT)
# Source directly from GitHub (shown for your own projects)
# source("https://raw.githubusercontent.com/olizardo/Jilbert-Distinction-Centrality/main/Functions/distinction.R")
# Example usage on a star graph
source("../Functions/distinction.R") # Sourcing locally for the site build
g <- make_star(7, mode = "undirected")
results <- distinction(g)
datatable(results, options = list(pageLength = 7, dom = 't'))The function computes status (\(s_i\)) using eigenvector centrality (processed component-wise for robustness), calculates the constraint (\(\kappa_i\)) by observing the average status of neighbors in a node-deleted subgraph, and finally computes the distinction score.
The mathematical formulation is: \[ \beta_i = \alpha s_i - \kappa_i \] Where \(\alpha\) is a scalar adjustment factor: \[ \alpha = \frac{\bar{\kappa}}{\bar{s}} \]
x: An igraph object representing the network.norm: A character string indicating the normalization method to use for status scores:
'max': Squares the status scores and divides by the maximum squared status.'one': Squares the status scores.'abm': Divides the absolute status scores by the maximum absolute status.'abs': Takes the absolute value of the status scores.digits: Number of decimal places for rounding the output.The function returns a data.frame containing: - n: Node names. - d: Raw distinction score (\(s_i - \kappa_i\)). - scd: Scaled distinction centrality (\(\alpha s_i - \kappa_i\)). - s: Status (eigenvector centrality). - u: Constraint (\(\kappa_i\)). - scalar: The \(\alpha\) adjustment factor.