Shortest Paths

• Shortest Paths

Shortest Paths

This example demonstrates how to find the shortest distance between two vertices on a weighted and unweighted graph.

To find the shortest path or distance between two nodes, we can use get_shortest_paths(). If we’re only interested in counting the unweighted distance, then we can do the following:

import igraph as ig
import matplotlib.pyplot as plt

# Find the shortest path on an unweighted graph
g = ig.Graph(
    6,
    [(0, 1), (0, 2), (1, 3), (2, 3), (2, 4), (3, 5), (4, 5)]
)

# g.get_shortest_paths() returns a list of vertex ID paths
results = g.get_shortest_paths(1, to=4, output="vpath")  # results = [[1, 0, 2, 4]]

if len(results[0]) > 0:
    # The distance is the number of vertices in the shortest path minus one.
    print("Shortest distance is: ", len(results[0])-1)
else:
    print("End node could not be reached!")

If the edges have weights, we pass them in as an argument. Note that we specify the output format as "epath", in order to receive the path as an edge list. This is used to calculate the length of the path.

# Find the shortest path on a weighted graph
g.es["weight"] = [2, 1, 5, 4, 7, 3, 2]

# g.get_shortest_paths() returns a list of edge ID paths
results = g.get_shortest_paths(
    0,
    to=5,
    weights=g.es["weight"],
    output="epath",
)
# results = [[1, 3, 5]]

if len(results[0]) > 0:
    # Add up the weights across all edges on the shortest path
    distance = 0
    for e in results[0]:
        distance += g.es[e]["weight"]
    print("Shortest weighted distance is: ", distance)
else:
    print("End node could not be reached!")

The output of these these two shortest paths are:

Shortest distance is:  3
Shortest weighted distance is:  8

The graph g with the shortest path from vertex 0 to vertex 5 highlighted.

Note

• get_shortest_paths() returns a list of lists becuase the to argument can also accept a list of vertex IDs. In that case, the shortest path to all each vertex is found and stored in the results array.

• If you’re interested in finding all shortest paths, take a look at get_all_shortest_paths().

In case you are wondering how the visualization figure was done, here’s the code:

import igraph as ig
import matplotlib.pyplot as plt

# Construct the graph
g = ig.Graph(
    6,
    [(0, 1), (0, 2), (1, 3), (2, 3), (2, 4), (3, 5), (4, 5)]
)
g.es["weight"] = [2, 1, 5, 4, 7, 3, 2]

# Get a shortest path along edges
results = g.get_shortest_paths(
    0,
    to=5,
    weights=g.es["weight"],
    output="epath",
)
# results = [[1, 3, 5]]

# Plot graph
g.es['width'] = 0.5
g.es[results[0]]['width'] = 2.5

fig, ax = plt.subplots()
ig.plot(
    g,
    target=ax,
    layout='circle',
    vertex_color='steelblue',
    vertex_label=range(g.vcount()),
    edge_width=g.es['width'],
    edge_label=g.es["weight"],
    edge_color='#666',
    edge_align_label=True,
    edge_background='white'
)