如何在R中用igraph或其他包模拟同配性/同质性图？

Great question! When working in R to simulate graphs with homophily (or assortativity), you've got solid options both within igraph and from specialized packages. Let's walk through the most practical approaches:

Using igraph for Homophily Simulation #

igraph has built-in tools to create graphs with assortative structure, with stochastic block models (SBMs) being the most straightforward for modeling homophily.

Stochastic Block Models (SBMs) #

SBMs group nodes into blocks where connections within blocks are far more frequent than between blocks—this directly mirrors the idea of homophily (nodes connecting to similar others). Use sample_sbm() to generate these graphs:

library(igraph)

# Define 2 groups of 50 nodes each
block_sizes <- c(50, 50)
# Set connection probabilities: high within groups, low between
block_probs <- matrix(c(0.8, 0.1, 0.1, 0.8), nrow = 2)

# Generate the SBM graph
sbm_graph <- sample_sbm(n = sum(block_sizes), pref.matrix = block_probs, block.sizes = block_sizes)

# Verify assortativity by group membership
assortativity_nominal(sbm_graph, membership(sbm_graph))

The pref.matrix controls connection likelihood between blocks—we set diagonal values (same-group connections) higher here to enforce strong homophily.

Rewiring Existing Graphs for Assortativity #

If you want to adjust an existing graph to add homophily, use rewire() with a custom probability function that favors same-attribute connections:

# Start with a random base graph
base_graph <- sample_gnm(n = 100, m = 200)
# Add a binary group attribute to nodes
V(base_graph)$group <- sample(c(0, 1), 100, replace = TRUE)

# Rewire edges to prioritize same-group connections
homophilous_graph <- rewire(
  base_graph,
  with = keeping_degseq(
    niter = 1000,
    prob = function(from, to) {
      # 80% chance to retain same-group edges, 20% for cross-group
      if (V(base_graph)$group[from] == V(base_graph)$group[to]) 0.8 else 0.2
    }
  )
)

Specialized R Packages for Advanced Homophily Simulation #

For more complex scenarios (like layered networks, weighted edges, or custom attribute-based biases), these packages offer tailored tools:

blockmodels #

Built explicitly for block models, this package supports layered, directed, and weighted SBMs—ideal for fine-tuning homophily structures:

library(blockmodels)

# Simulate a binary undirected SBM with 2 blocks
bm <- BM_bernoulli("SBM", n = 100, k = 2)
bm$sampling()

# Convert the result to an igraph object
bm_graph <- graph_from_adjacency_matrix(bm$model_parameters$adjacency, mode = "undirected")

statnet (via ergm) #

The ergm package from the statnet suite lets you simulate networks using exponential random graph models, where you can explicitly include homophily terms (e.g., nodematch() to reward same-attribute connections):

library(ergm)

# Initialize a network with a binary group attribute
n <- 100
net <- network.initialize(n, directed = FALSE)
set.vertex.attribute(net, "group", sample(c(0, 1), n, replace = TRUE))

# Define an ERGM with edges + homophily term
homophily_model <- ergm(net ~ edges + nodematch("group"))

# Simulate a graph from the model
simulated_net <- simulate(homophily_model)

netdiffuseR #

While focused on diffusion processes, this package includes simulate_net() to generate networks with configurable homophily bias:

library(netdiffuseR)

# Create node data with a binary group attribute
nodes <- data.frame(group = sample(c(0, 1), 100, replace = TRUE))

# Simulate network with 70% homophily bias (prioritize same-group connections)
hom_net <- simulate_net(nodes, homophily = 0.7, randomness = 0.3)

# Convert to an igraph object
hom_igraph <- graph_from_adjacency_matrix(hom_net, mode = "undirected")

内容的提问来源于stack exchange，提问作者user321627