Lack of Support for Directed Graph Visualization with Arrowheads

[MohammadRaziei]

The pygsp library currently does not support the visualization of directed graphs with arrowheads on edges. When using the plot_graph function to visualize a graph created from a directed adjacency matrix, the edges are displayed as undirected lines without any indication of directionality (e.g., arrowheads).

For example, consider the following directed graph defined by the adjacency matrix:

import numpy as np
import pygsp as gsp

# Define a directed graph using an adjacency matrix
W = np.array([
    [0, 3, 7, 0, 0],  # Node 1 → Node 2 (weight=3), Node 1 → Node 3 (weight=7)
    [0, 0, 0, 5, 0],  # Node 2 → Node 4 (weight=5)
    [0, 0, 0, 2, 0],  # Node 3 → Node 4 (weight=2)
    [0, 0, 0, 0, 4],  # Node 4 → Node 5 (weight=4)
    [0, 0, 0, 0, 0]   # Node 5 has no outgoing edges
])

G = gsp.graphs.Graph(W)  # Create a graph from the adjacency matrix
G.set_coordinates(seed=42)  # Set coordinates for visualization

When visualizing this graph using gsp.plotting.plot_graph(G), the edges are displayed as undirected lines, even though the adjacency matrix explicitly defines directed edges.

Expected Behavior:

• The edges should be displayed with arrowheads to indicate the direction of each edge.
• The visualization should clearly distinguish between directed and undirected graphs.

Current Behavior:

• The edges are displayed as undirected lines, regardless of the adjacency matrix being directed or undirected.

Proposed Solution:

• Add an optional parameter (e.g., directed=True) to the plot_graph function to enable visualization of directed graphs with arrowheads.
• Use Matplotlib's arrow functionality to draw directed edges with customizable arrow styles (e.g., arrowheads, colors, widths).

Workaround:
Currently, users can manually draw directed edges using Matplotlib's arrow function, but this requires additional code and is not integrated into the plot_graph functionality.

Example Workaround Code:

import matplotlib.pyplot as plt

for i, (u, v) in enumerate(G.get_edge_list()):
    x_start, y_start = G.coords[u]
    x_end, y_end = G.coords[v]
    plt.arrow(x_start, y_start, x_end - x_start, y_end - y_start,
              head_width=0.05, head_length=0.1, fc='gray', ec='gray',
              length_includes_head=True)
plt.show()

This workaround demonstrates how directed edges can be visualized, but it would be ideal to have this functionality built into pygsp.