# Minimum Spanning Trees ¶

# Minimum Spanning Trees¶

This example shows how to generate a minimum spanning tree from an input graph using `spanning_tree()`

. If you only need a regular spanning tree, check out Spanning Trees.

We start by generating a grid graph with random integer weights between 1 and 20:

```
import random
import igraph as ig
import matplotlib.pyplot as plt
# Generate grid graph with random weights
random.seed(0)
g = ig.Graph.Lattice([5, 5], circular=False)
g.es["weight"] = [random.randint(1, 20) for _ in g.es]
```

We then call `spanning_tree()`

, making sure to pass in the randomly generated weights.

```
# Generate spanning tree
spanning_tree = g.spanning_tree(weights=None, return_tree=False)
```

Finally, we generate the plot the graph and visualise the spanning tree. We also print out the sum of the edges in the MST.

```
# Plot graph
g.es["color"] = "lightgray"
g.es[spanning_tree]["color"] = "midnightblue"
g.es["width"] = 0.5
g.es[spanning_tree]["width"] = 3.0
fig, ax = plt.subplots()
ig.plot(
g,
target=ax,
layout=layout,
vertex_color="lightblue",
edge_width=g.es["width"]
)
plt.show()
# Print out minimum edge weight sum
print("Minimum edge weight sum:", sum(g.es[mst_edges]["weight"]))
```

The final plot looks like this:

… and the output looks like this:

```
Minimum edge weight sum: 136
```

Note

The randomised weights may vary depending on the machine that you run this code on.