Installation

genet can be installed via the install_github function in the devtools package.

library(devtools)
install_github("aagrande/genet")

Example: generating scale-free networks

Before invoking the generator via genet, we define:

• the number of communities K and node types L;
• a target community structure as encoded by the community assignments;
• a target degree distribution as encoded by a degree sequence with target degrees for each node type.

Depending on the application of interest, users can input their custom community structure. Here, for simplicity, we will generate a balanced structure via the generate_balanced_assignments function. This function randomly assigns each node type to K_each communities such that: no types have identical assignments; all communities have at least one type; and the resulting graph of type-to-type interactions is connected.

library(genet)
K <- 100
L <- 200
Z <- generate_balanced_assignments(K, L, K_each = 5)

For the target degree distribution, we choose a scale-free distribution: , . We choose the minimum and maximum degree, as well as the power law’s exponent , so that the expected degree is approximately 15.

d_min <- 3
d_max <- 500
alpha <- 1.937
as.numeric(dpower_law(3:500, alpha, d_min, d_max) %*% 3:500)

## [1] 15.00011

To closely reproduce the power-law distribution, we set the target degree sequence equal to the -quantiles of the distribution. Also, we adjust the type cardinalities so that the empirical distribution complies with the power law.

target_degrees <- qpower_law(seq(0, 1, length.out = L), alpha, d_min, d_max)
probs <- dpower_law(target_degrees, alpha, d_min, d_max)
ratios <- probs / min(probs)
cards <- round(ratios * 2)

We can now generate networks with the desired community structure and target degree centrality distribution. We set dc = TRUE to specify that we target the degree centrality (as opposed to the eigencentrality).

g <- genet(n = 10, assignments = Z, cards = cards, multiedges = TRUE, dc = TRUE,
           target_centrality = target_degrees)

The output of genet is a list of igraph graph objects. The first graph has the following number of nodes and edges:

cat("# of nodes = ", igraph::vcount(g[[1]]), "\n# of edges = ", igraph::ecount(g[[1]]), sep = "")

## # of nodes = 148611
## # of edges = 904523

Its empirical degree distribution is plotted below (the target power-law is represented in blue).

References

• Grande and Feng, 2023. Principled and Scalable Network Generation with Built-in Community Structure and Target Centrality Measures.