用节点属性模拟 ERGM

Question

我想知道是否有可能模拟来自 ERGM 分布的网络，其中节点具有属性。例如，如果我想模拟一个网络，其中具有相似属性的节点之间的三角形更有可能出现，我会这样做：

library(ergm)

g_sim = simulate(network(n, directed=FALSE) ~ triangles + nodematch, 
                 nsim=1, 
                 coef=thetas)

但问题是这些依赖于节点属性的统计数据（即像nodematch）需要参数，我没有参数，因为网络事先不存在（我正在尝试模拟它）。

这怎么可能呢？

Answer 1

这样的事情行得通吗？

library(ergm)

                                        # Initialize an empty network with N nodes
N <- 50
g <- network(1, directed = FALSE)
add.vertices(g, N - network.size(g))

                                        # Make up a node classification to go with nodematch
type <- rbinom(N, 1, .25)
g %v% "type" <- ifelse(type, "green", "blue")

                                        # Set the parameters of the model.
                                        # Use large coefficients to make the result clear.
                                        # These coefficients should set the base density and the
                                        # density of edges between nodes of the same type.
thetas <- c(-2.5, 2.5)

                                        # Simulate one network
                                        # I'm using edges instead of triangles because of the
                                        # tendancy towards degeneracy with triangles (my first attempt
                                        # had a density of 1.0)
g_sim <- simulate(
    g ~ edges + nodematch("type"), 
    nsim = 1, 
    coef = thetas
)

                                        # Plot to be sure. There should be many more edges between
                                        # nodes of the same color than nodes of different colors.
plot(g_sim, vertex.col = g %v% "type")

                                        # Are the coefficients similar to what they should be?
m <- ergm(g_sim ~ edges + nodematch("type"))
summary(m)