I made this random graph/network in R:

```
set.seed(123)
library(igraph)
# Create random graph
graph <- erdos.renyi.game(21, 0.3, type=c("gnp", "gnm"), directed = FALSE, loops = FALSE)
```

Then, I tried to create a random connected subgraph:

```
# Get the edges of the random subgraph
random_edges <- sample(E(graph), 10)
# Create subgraph from the random edges
subgraph <- subgraph.edges(graph, random_edges)
par(mfrow = c(1,2))
# Plot the subgraph
plot(subgraph, main = "random subgraph")
plot(graph, main = "original graph")
```

**My Question:** When I look at the random subgraph, I see that "node 4" is connected to "node 10" - but in the original graph, "node 4" and "node 10" are not connected to each other.

Can someone please show me how to fix this?

Thanks!