Usage Examples

This section provides examples of how to use the gdar package for creating graphs, visualizing connectivity, and fitting the Graph Diffusion Autoregressive (GDAR) model. The GitHub repository also contains a demo jupyter notebook that demonstrates these and additional functionalities in more detail.

Creating a Structural Connectivity Graph

The gdar package provides functions for creating structural connectivity graphs, which the GDAR model uses to estimate network communication dynamics. You can create graphs from:

• A user-defined edge list

• Node positions and built-in graph generator methods

First, let’s create a graph from a simple edge list:

from gdar.graph import Graph

# Define edges
edge_list = [(0, 1), (0, 2), (1, 2), (1, 3), (2, 3), (3, 4)]

# Create graph
graph = Graph()
graph.generate_from_edge_list(edge_list)

Visualizing the Graph

To visualize the graph, use the plot_graph function from the visualization module:

from gdar.visualization import plot_graph
from matplotlib import pyplot as plt

node_positions = {
    0: (0, 0),
    1: (1, 0),
    2: (1, 1),
    3: (0, 1),
    4: (0.5, 1.5)
}

graph.set_node_position_name(node_positions)
plot_graph(
    graph,
    directed=False,
    node_size=500,
    node_color='lightblue',
    edge_color='gray',
    width=10,
    with_labels=True
)
plt.show()

Adding Edges to an Existing Graph

You can add edges manually:

edges_to_add = [(0, 3), (2, 4)]
graph.add_edges(edges_to_add)

# Visualize updated graph
plot_graph(graph, directed=False, node_size=500, node_color='lightblue', edge_color='gray')
plt.show()

Creating a Graph from Node Positions

For large arrays or multiple brain regions, you can use graph generator methods:

import pickle
from gdar.graph import Graph

# Load node positions
with open('demo_files/node_positions.pkl', 'rb') as f:
    node_positions = pickle.load(f)

# Create proximity-based graph
graph2 = Graph()
graph2.proximity_graph(node_positions, dist_th=2)

# Visualize
plot_graph(graph2, directed=False, node_size=500, node_color='lightblue')
plt.show()

Fitting the GDAR Model

Once a graph is created, fit the GDAR model to your time-series data:

import numpy as np
from gdar.gdar_model import GDARModel

# Generate toy data
np.random.seed(42)
T = 1000  # number of time points
N = len(node_positions)
data = np.random.randn(N, T)

# Initialize GDAR model
model_order = 5
gdar_model = GDARModel(graph=graph2, K=model_order)

# Fit model
coefficients = gdar_model.fit_gdar(data)
print(f'Fitted coefficients shape: {coefficients.shape}')