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Generate Linearized Chord Diagram (LCD) Graphs

Source: R/lcd_graphs.R
lcd_graphs.Rd

[Experimental]

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.

Value

An igraph object representing the generated LCD graph.

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.

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)