Package 'ig.degree.betweenness'

Community structure detection based on node degree centrality and edge betweenness

Description

Referred to as the "Smith-Pittman" algorithm in Smith et al (2024). This algorithm detects communities by calculating the degree centrality measures of nodes and edge betweenness.

Usage

cluster_degree_betweenness(graph)

Arguments

graph

The graph to analyze

Details

This can be thought of as an alternative version of igraph::cluster_edge_betweeness().

The function iteratively removes edges based on their betweenness centrality and the degree of their adjacent nodes. At each iteration, it identifies the edge with the highest betweenness centrality among those connected to nodes with the highest degree.It then removes that edge and recalculates the modularity of the resulting graph. The process continues until all edges have been assessed or until no further subgraph can be created with the optimal number of communites being chosen based on maximization of modularity.

Value

An igraph "communities" object with detected communities via the Smith-Pittman algorithm.

References

Smith et al (2024) "Centrality in Collaboration: A Novel Algorithm for Social Partitioning Gradients in Community Detection for Multiple Oncology Clinical Trial Enrollments", https://doi.org/10.48550/arXiv.2411.01394

Examples

library(igraphdata)
data("karate")
ndb <- cluster_degree_betweenness(karate)
plot(
ndb,
karate,
main= "Degree-Betweenness Clustering"
)

ndb


data("UKfaculty")
# Making graph undirected so it looks nicer when its plotted
uk_faculty <- UKfaculty |>
  igraph::as.undirected()

ndb <- cluster_degree_betweenness(uk_faculty)

plot(
  ndb,
  uk_faculty,
  main= "Smith-Pittman Clustering for UK Faculty"
)

---

Analyze Degree Balance of a Graph

Description

Computes and summarizes vertex degree distributions for an igraph object. For directed graphs, the function reports in-degree and out-degree statistics, including their correlation and mean values. For undirected graphs, only overall degree statistics are reported.

Usage

degree_balance(g)

Arguments

g	An igraph graph object.

Details

If the graph is directed (see igraph::is_directed()), the function:

• Computes in-degree and out-degree for each vertex.

• Prints summary statistics for both distributions.

• Reports the correlation between in-degree and out-degree.

• Reports mean in-degree and mean out-degree.

If the graph is undirected, the function:

• Computes the degree for each vertex.

• Prints summary statistics of the degree distribution.

Value

A list containing:

• out_degree Numeric vector of out-degrees (directed graphs only).

• in_degree Numeric vector of in-degrees (directed graphs only).

• degree Numeric vector of degrees (undirected graphs only).

Examples

library(igraph)
library(ig.degree.betweenness)

# Directed graph example
g_directed <- make_ring(10, directed = TRUE)
degree_balance(g_directed)

# Undirected graph example
g_undirected <- make_ring(10)
degree_balance(g_undirected)

---

Generate Linearized Chord Diagram (LCD) Graphs

Description

A family of functions to generate networks based on the Linearized Chord Diagram (LCD) model using preferential attachment. The suite includes the standard LCD model as well as variants that introduce bidirectional edges, alternating direction attachment, and mixed degree preferences.

Usage

lcd_graph(n, m = 1, directed = TRUE)

lcd_graph_bidirectional(n, m = 1, directed = TRUE, bidirectional_prob = 0.5)

lcd_graph_alternating(n, m = 1, directed = TRUE)

lcd_graph_mixed(n, m = 1, directed = TRUE, out_weight = 0.5)

Arguments

n	Integer. The total number of vertices (nodes) in the generated graph.
m	Integer. The number of edges each new node adds during its time step. Defaults to 1.
directed	Logical. Whether the generated graph should be directed. Defaults to TRUE.
bidirectional_prob	Numeric. The probability (between 0 and 1) of adding a reverse edge (target -> source) when generating bidirectional graphs. Used only in lcd_graph_bidirectional. Defaults to 0.5.
out_weight	Numeric. The probability weight (between 0 and 1) given to the out-degree pool versus the in-degree pool. Used only in lcd_graph_mixed. Defaults to 0.5.

Details

The standard lcd_graph function builds a network step-by-step. At each time step t from 1 to n, a new node is added and generates m edges. The target of each edge is chosen preferentially based on the degree of the existing nodes.

The package also provides three variations:

• lcd_graph_bidirectional: Adds a primary edge and, with a specified probability, simultaneously adds a reverse edge.

• lcd_graph_alternating: Alternates between using out-degree and in-degree pools for preferential attachment targets.

• lcd_graph_mixed: Chooses between out-degree and in-degree pools for attachment based on a weighted probability.

Value

An igraph object representing the generated LCD graph.

References

Barabási, A.-L. (2016). Network Science. Cambridge University Press. Chapter 5: The Barabási-Albert Model. https://networksciencebook.com/chapter/5

Examples

# Generate a standard directed LCD graph with 100 nodes and 2 edges per step
g1 <- lcd_graph(n = 100, m = 2)

# Generate a graph where reverse edges appear 30% of the time
g2 <- lcd_graph_bidirectional(n = 100, m = 1, bidirectional_prob = 0.3)

# Generate a graph alternating between in-degree and out-degree attachment
g3 <- lcd_graph_alternating(n = 100, m = 3)

# Generate a mixed graph favoring out-degree attachment 70% of the time
g4 <- lcd_graph_mixed(n = 100, m = 2, out_weight = 0.7)

---

Oncology Clinical Trial Referral Network

Description

A simulated oncology clinical trial referral network from a major research hospital. For the purpose of identifying collaboration networks between oncologists, this dataset only includes referrals of patients who were enrolled in more than one clinical trial. This includes 389 patients enrolled in 288 clinical trials.

Usage

oncology_network

Format

A igraph object (e.g. representing the oncology clinical trial referral network. The structure includes:

nodes

Oncologists or clinical trials (depending on network structure).

edges

Referral links between nodes, based on shared patient enrollment across trials.

Details

Clinical trials are categorized by intervention type, including targeted therapies (prefixed with "T:") and immunotherapies (prefixed with "I:"). There are 16 distinct intervention types (nodes) and 470 patient referrals (edges) in the network.

Source

Simulated data based on oncology clinical trial enrollment patterns.

---

Visualize Node Degree Distribution in a Network Graph

Description

Generates a horizontal bar‐style plot of node degrees for an igraph network. For undirected graphs, it shows each node’s total degree. For directed graphs, it displays in‐degrees (as negative bars) alongside out‐degrees.

Usage

plot_node_degrees(graph)

Arguments

graph

An igraph object. Can be either directed or undirected.

Details

This function computes:

Total degree

Number of edges incident on each node (for undirected graphs).

In‐degree

Number of incoming edges per node (for directed graphs).

Out‐degree

Number of outgoing edges per node (for directed graphs).

For directed graphs, in‐degrees are negated so that bars extend leftward, providing an immediate visual comparison to out‐degrees.

Internally, it uses:

• igraph::degree() to compute degrees,

• dplyr and tidyr for reshaping the data,

• ggplot2 for plotting.

Value

A ggplot object:

• Undirected graphs: A bar for each node showing its total degree.

• Directed graphs: Split bars per node with negative values for in‐degree (pointing left) and positive values for out‐degree (pointing right).

Customization

You can modify the returned ggplot with additional layers, themes, or labels. For example, to add a title or change colors:

plot_node_degrees(g) +
  ggtitle("Degree Distribution") +
  scale_fill_manual(values = c("in_degree" = "steelblue", "out_degree" = "salmon"))

Examples

library(ig.degree.betweenness)
library(igraphdata)
data("karate")
data("oncology_network")
plot_node_degrees(oncology_network)
plot_node_degrees(karate)

---

Plot Simplified Edgeplot

Description

This function generates a simplified edge plot of an igraph object, optionally highlighting communities if provided.

Usage

plot_simplified_edgeplot(graph, communities = NULL, edge.arrow.size = 0.2, ...)

Arguments

graph	igraph object
communities	optional; A communities object
edge.arrow.size	edge.arrow size arg. See ?igraph::plot.igraph for more details
...	other arguments to be passed to the plot() function

Details

This function is ideally for networks with a low number of nodes having varying numbers of connection and self loops. See the example for a better visual understanding.

Value

No return value, called for side effects.

Examples

# Load the igraph package
library(igraph)
library(ig.degree.betweenness)
# Set parameters
num_nodes <- 15    # Number of nodes (adjust as needed)
initial_edges <- 1   # Starting edges for preferential attachment

# Create a directed, scale-free network using the Barabási-Albert model
g <- sample_pa(n = num_nodes, m = initial_edges, directed = TRUE)

# Introduce additional edges to high-degree nodes to accentuate popularity differences
num_extra_edges <- 350   # Additional edges to create more popular nodes
set.seed(123)           # For reproducibility

for (i in 1:num_extra_edges) {
  # Sample nodes with probability proportional to their degree (to reinforce popularity)
  from <- sample(V(g), 1, prob = degree(g, mode = "in") + 1)  # +1 to avoid zero probabilities
  to <- sample(V(g), 1)

  # Ensure we don't add the same edge repeatedly unless intended, allowing self-loops
  g <- add_edges(g, c(from, to))
}

# Add self-loops to a subset of nodes
num_self_loops <- 5
for (i in 1:num_self_loops) {
  node <- sample(V(g), 1)
  g <- add_edges(g, c(node, node))
}



ig.degree.betweenness::plot_simplified_edgeplot(g,main="Simulated Data")

---

Prepared Unlabeled Graph to work with Degree-Betweenness Algorithm

Description

Presently, cluster_degree_betweenness() function only works with labeled graphs. prep_unlabeled_graph() is a utility function that gives an unlabeled graph labels which are string values of their vertices.

Usage

prep_unlabeled_graph(graph)

Arguments

graph

an unlabeled graph.

Value

An "igraph" object with named vertices.

See Also

cluster_degree_betweenness() which this function aids.

Examples

library(igraph)
library(igraphdata)
library(ig.degree.betweenness)
data("UKfaculty")
# Making graph undirected so it looks nicer when its plotted
uk_faculty <- prep_unlabeled_graph(UKfaculty) |>
  as.undirected()

ndb <- cluster_degree_betweenness(uk_faculty)

plot(
ndb,
uk_faculty,
main= "Node Degree Clustering"
)

ndb

---