How to define a graph using a distance matrix in igraph? (R)

Question

I have a distance matrix from N points that I'd like to use to create a fully connected graph between N nodes.

So far I've tried the graph_from_adjacency_matrix function, but if my distance matrix is:

      [,1] [,2] [,3]
[1,]    0   10    3
[2,]   10    0    2
[3,]    3    2    0

then I create the graph:

g3 =  graph_from_adjacency_matrix(dist_matrix, weighted=TRUE, mode="undirected")

But when I plot it, node 2 doesn't seem to be further from node 1 than node 3 is.

Is there a way to define the graph from this matrix and then plot it (with nodes closer to each other when the distance is smaller and vice versa)?