Graph/Network Analysis Based on 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.
Version 0.1.1 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)
Using the Marvel Cinematic Universe movie network (undirected, connected
graph) and 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-based neighborhood),
L1centLOC()
(local L1 centrality), L1centEDGE()
(multiscale edge representation), and Lorenz_plot()
(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.
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).
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. Manuscript. 2024b.