L1centrality

Graph/Network Analysis Based on L1 Centrality

What is L₁ centrality?

L₁ centrality is a new centrality measure that assesses the prominence of vertices in an undirected and connected graph (Kang and Oh 2024a). It properly handles graphs that have weights assigned to both vertices and edges. Based on this centrality measure, several graphical and multiscale analysis tools are developed.

There are analogous measures for strongly connected directed graphs: the L₁ centrality and L₁ prestige (Kang and Oh 2024b). The former one quantifies the prominence of vertices in giving choices, while the latter evaluates the prominence in receiving choices. Multiscale analysis tools are developed from these measures as well.

These measures are further extended to assess the prominence of a group of vertices: the group L₁ centrality and group L₁ prestige measures are developed for this purpose (Kang 2025).

How can I get L1centrality?

Version 0.3.1 of this package is available on CRAN:

install.packages("L1centrality")
library(L1centrality)

You can install the development version (currently equivalent to the CRAN version) of L1centrality via:

devtools::install_github("seungwoo-stat/L1centrality")
library(L1centrality)

How do I use it?

Using the Marvel Cinematic Universe movie network (undirected, connected graph) and the L₁ centrality function L1cent() provided via this package, we can identify movies with high L₁ centrality, i.e., movies that are central in the given network.

library(L1centrality)
L1cent(MCUmovie) |> 
  sort(decreasing = TRUE) |> 
  head()
#>  Avengers: Infinity War       Avengers: Endgame            The Avengers 
#>               1.0000000               0.6939885               0.5269421 
#>              Iron Man 2 Avengers: Age of Ultron  Spider-Man: Homecoming 
#>               0.4113450               0.3865311               0.3691427

There are other useful functions built upon the L₁ centrality and L₁ prestige measures: L1centMDS() (target plot), L1centNB() (L₁ centrality/prestige-based neighborhood), L1centLOC() (local L₁ centrality/prestige), L1centEDGE() (multiscale edge representation), L1centGROUP() (group L₁ centrality/prestige), and Lorenz_plot() & Gini() (group heterogeneity plot and index).

Refer to the package documentation for an overview of the support range for each function.

?`L1centrality-package`

Moreover, two undirected and connected network data are provided: MCUmovie (Marvel Cinematic Universe movie network) and rokassembly21 (Republic of Korea’s 21st National Assembly bill cosponsorship network). See the document for further details.

Where can I learn more?

Visit this repo for code to reproduce the figures and analysis from the paper Kang and Oh (2024a) and this repo for code to reproduce the figures and analysis from the paper Kang and Oh (2024b). This repo contains code for analysis using group L₁ centrality and prestige measures (Kang 2025; Ch.6).

References

Seungwoo Kang and Hee-Seok Oh. On a Notion of Graph Centrality Based on L₁ Data Depth. arXiv preprint arXiv:2404.13233. 2024a.

Seungwoo Kang and Hee-Seok Oh. L₁ Prominence Measures for Directed Graphs. arXiv preprint arXiv:2408.12078. 2024b.

Seungwoo Kang. Topics in Non-Euclidean Dimension Reduction. PhD thesis, Seoul National University. 2025.