我在R中有一个网络图：

set.seed(123)
library(igraph)

# Define a vector of names
names <- c("John", "Alex", "Jason", "Matt", "Tim", "Luke", "Shawn", "Henry", "Steven", "Scott", "Adam", "Jeff", "Connor", "Peter", "Andrew", "Dave", "Daniel", "Benjamin", "Joseph", "Martin")

# Create an empty graph with 20 nodes
g <- make_empty_graph(20)

# Add random edges between nodes to represent friendships
set.seed(123)  # for reproducibility
num_edges <- 40
edge_list <- sample(names, size = num_edges * 2, replace = TRUE)
edge_list <- matrix(edge_list, ncol = 2, byrow = TRUE)
g <- graph_from_edgelist(edge_list, directed = FALSE)

# Set the node names to be the names vector
V(g)$name <- names

# Plot the graph
plot(g, vertex.label.cex = 0.7, vertex.label.color = "black", vertex.label.dist = 2)

**我的问题：**假设我从约翰开始--我想做一个随机子图，使得：

• “最大度”为= n
• 子图中的“节点数”为= m
• 子图中的所有节点都可以追溯到John

使用前面的问题R: All Nodes of Degree "N" that can be reached from Some Node，我尝试解决这个问题：

all_distances = as.numeric(max(distances(g, "John")))
max_degree =  as.numeric(sample(0:all_distances, 1))
frame_with_max_degree = data.frame(unlist(ego(g, max_degree, "John")))
number_of_nodes = as.numeric(sample(0:nrow(frame_with_max_degree), 1))

**我的问题：**但是从这里开始，我不确定如何随机选择单个节点number_of_nodes，使得所有这些节点都必然连接到“John”。

例如，假设n = 3，m = 2：我不想创建具有“约翰”、“杰森”和“史蒂文”的子图-因为即使“杰森和史蒂文”可能在随机生成的半径内，“杰森和史蒂文”仍然不直接连接到“约翰.”
有人能教我怎么做吗？
谢谢！