Add slipnet analysis: depth vs topology correlation study

Analysis shows no significant correlation between conceptual depth
and hop distance to letter nodes (r=0.281, p=0.113). Includes
Python scripts, visualizations, and LaTeX paper.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

slipnet_analysis/plot_depth_distance_correlation.py

@@ -0,0 +1,108 @@
+"""
+Plot correlation between minimum hops to letter nodes and conceptual depth.
+"""
+
+import json
+import matplotlib
+matplotlib.use('Agg')  # Non-interactive backend
+import matplotlib.pyplot as plt
+import numpy as np
+from scipy import stats
+
+def load_slipnet(filepath):
+    with open(filepath, 'r') as f:
+        return json.load(f)
+
+def main():
+    filepath = r'C:\Users\alexa\copycat\slipnet_analysis\slipnet.json'
+    data = load_slipnet(filepath)
+
+    # Extract data points (excluding letter nodes themselves)
+    names = []
+    depths = []
+    hops = []
+    is_unreachable = []  # Track which nodes are unreachable
+
+    for node in data['nodes']:
+        name = node['name']
+        depth = node['conceptualDepth']
+        path_info = node.get('minPathToLetter', {})
+        hop_count = path_info.get('hops')
+        nearest = path_info.get('nearestLetter')
+
+        # Skip letter nodes (hops 0)
+        if hop_count is not None and hop_count > 0:
+            names.append(name)
+            depths.append(depth)
+            hops.append(hop_count)
+            # Unreachable nodes have no nearestLetter
+            is_unreachable.append(nearest is None)
+
+    # Convert to numpy arrays
+    depths = np.array(depths)
+    hops = np.array(hops)
+    is_unreachable = np.array(is_unreachable)
+
+    # Compute correlation
+    correlation, p_value = stats.pearsonr(depths, hops)
+    spearman_corr, spearman_p = stats.spearmanr(depths, hops)
+
+    # Create the plot
+    fig, ax = plt.subplots(figsize=(10, 8))
+
+    # Scatter plot with jitter for overlapping points
+    jitter = np.random.normal(0, 0.08, len(hops))
+
+    # Plot reachable nodes in blue
+    reachable_mask = ~is_unreachable
+    ax.scatter(depths[reachable_mask], hops[reachable_mask] + jitter[reachable_mask],
+               alpha=0.7, s=100, c='steelblue', edgecolors='navy', label='Reachable')
+
+    # Plot unreachable nodes in red
+    if np.any(is_unreachable):
+        ax.scatter(depths[is_unreachable], hops[is_unreachable] + jitter[is_unreachable],
+                   alpha=0.7, s=100, c='crimson', edgecolors='darkred', label='Unreachable (2×max)')
+
+    # Add labels to each point
+    for i, name in enumerate(names):
+        ax.annotate(name, (depths[i], hops[i] + jitter[i]), fontsize=8, alpha=0.8,
+                    xytext=(5, 5), textcoords='offset points')
+
+    # Add trend line
+    z = np.polyfit(depths, hops, 1)
+    p = np.poly1d(z)
+    x_line = np.linspace(min(depths), max(depths), 100)
+    ax.plot(x_line, p(x_line), "r--", alpha=0.8, label=f'Linear fit (y = {z[0]:.3f}x + {z[1]:.2f})')
+
+    # Labels and title
+    ax.set_xlabel('Conceptual Depth', fontsize=12)
+    ax.set_ylabel('Minimum Hops to Letter Node (Erdos-style)', fontsize=12)
+    ax.set_title('Correlation: Conceptual Depth vs Hops to Nearest Letter\n'
+                 f'Pearson r = {correlation:.3f} (p = {p_value:.4f}), '
+                 f'Spearman rho = {spearman_corr:.3f} (p = {spearman_p:.4f})',
+                 fontsize=11)
+
+    ax.legend(loc='upper left')
+    ax.grid(True, alpha=0.3)
+    max_hops = int(max(hops))
+    ax.set_yticks(range(1, max_hops + 1))
+    ax.set_ylim(0.5, max_hops + 0.5)
+
+    # Print statistics
+    print(f"Number of nodes with paths (excluding letters): {len(names)}")
+    print(f"\nPearson correlation: r = {correlation:.4f}, p-value = {p_value:.6f}")
+    print(f"Spearman correlation: rho = {spearman_corr:.4f}, p-value = {spearman_p:.6f}")
+    print(f"\nLinear regression: hops = {z[0]:.4f} * depth + {z[1]:.4f}")
+
+    print("\nData points:")
+    print(f"{'Node':<30} {'Depth':<10} {'Hops':<10}")
+    print("-" * 50)
+    for name, depth, hop in sorted(zip(names, depths, hops), key=lambda x: (x[2], x[1])):
+        print(f"{name:<30} {depth:<10.1f} {hop:<10}")
+
+    plt.tight_layout()
+    plt.savefig(r'C:\Users\alexa\copycat\slipnet_analysis\depth_hops_correlation.png', dpi=150)
+    print(f"\nPlot saved to: C:\\Users\\alexa\\copycat\\slipnet_analysis\\depth_hops_correlation.png")
+
+if __name__ == '__main__':
+    main()