Add comprehensive centrality analysis to slipnet study
Key finding: Eccentricity is the only metric significantly correlated with conceptual depth (r=-0.380, p=0.029). Local centrality measures (degree, betweenness, closeness) show no significant correlation. New files: - compute_centrality.py: Computes 8 graph metrics - centrality_comparison.png: Visual comparison of all metrics - Updated paper with full analysis Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
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Alex Linhares
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slipnet_analysis/compute_centrality.py
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slipnet_analysis/compute_centrality.py
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"""
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Compute various centrality and graph metrics for slipnet nodes.
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Compare correlations with conceptual depth.
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"""
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import json
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import numpy as np
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import networkx as nx
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from scipy import stats
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import matplotlib
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matplotlib.use('Agg')
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import matplotlib.pyplot as plt
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def load_slipnet(filepath):
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with open(filepath, 'r') as f:
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return json.load(f)
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def build_graph(data):
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"""Build an undirected graph from slipnet JSON."""
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G = nx.Graph()
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for node in data['nodes']:
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G.add_node(node['name'], depth=node['conceptualDepth'])
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for link in data['links']:
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G.add_edge(link['source'], link['destination'])
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return G
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def get_letter_nodes():
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return set(chr(i) for i in range(ord('a'), ord('z') + 1))
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def compute_all_metrics(G):
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"""Compute all centrality and graph metrics."""
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metrics = {}
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# Degree centrality
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metrics['degree'] = nx.degree_centrality(G)
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# Betweenness centrality
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metrics['betweenness'] = nx.betweenness_centrality(G)
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# Closeness centrality
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metrics['closeness'] = nx.closeness_centrality(G)
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# Eigenvector centrality (may fail on disconnected graphs)
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try:
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metrics['eigenvector'] = nx.eigenvector_centrality(G, max_iter=1000)
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except nx.PowerIterationFailedConvergence:
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# For disconnected graphs, compute on largest component
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largest_cc = max(nx.connected_components(G), key=len)
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subG = G.subgraph(largest_cc)
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eig = nx.eigenvector_centrality(subG, max_iter=1000)
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# Assign 0 to disconnected nodes
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metrics['eigenvector'] = {n: eig.get(n, 0.0) for n in G.nodes()}
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# PageRank
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metrics['pagerank'] = nx.pagerank(G)
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# Clustering coefficient
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metrics['clustering'] = nx.clustering(G)
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# Average neighbor degree
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metrics['avg_neighbor_degree'] = nx.average_neighbor_degree(G)
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# Eccentricity (only for connected components)
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metrics['eccentricity'] = {}
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for component in nx.connected_components(G):
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subG = G.subgraph(component)
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ecc = nx.eccentricity(subG)
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metrics['eccentricity'].update(ecc)
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# Disconnected nodes get max eccentricity + 1
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max_ecc = max(metrics['eccentricity'].values()) if metrics['eccentricity'] else 0
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for n in G.nodes():
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if n not in metrics['eccentricity']:
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metrics['eccentricity'][n] = max_ecc + 1
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return metrics
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def main():
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filepath = r'C:\Users\alexa\copycat\slipnet_analysis\slipnet.json'
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data = load_slipnet(filepath)
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print(f"Loaded slipnet with {data['nodeCount']} nodes and {data['linkCount']} links")
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# Build graph
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G = build_graph(data)
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print(f"Built graph with {G.number_of_nodes()} nodes and {G.number_of_edges()} edges")
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# Get letter nodes
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letter_nodes = get_letter_nodes()
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# Compute all metrics
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print("\nComputing centrality metrics...")
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metrics = compute_all_metrics(G)
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# Extract non-letter nodes with their depths
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names = []
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depths = []
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for node in data['nodes']:
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if node['name'] not in letter_nodes:
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names.append(node['name'])
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depths.append(node['conceptualDepth'])
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depths = np.array(depths)
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# Compute correlations for each metric
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print("\n" + "=" * 80)
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print("CORRELATION ANALYSIS: Conceptual Depth vs Graph Metrics")
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print("=" * 80)
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results = []
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metric_names = {
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'degree': 'Degree Centrality',
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'betweenness': 'Betweenness Centrality',
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'closeness': 'Closeness Centrality',
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'eigenvector': 'Eigenvector Centrality',
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'pagerank': 'PageRank',
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'clustering': 'Clustering Coefficient',
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'avg_neighbor_degree': 'Avg Neighbor Degree',
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'eccentricity': 'Eccentricity'
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}
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for metric_key, metric_label in metric_names.items():
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metric_values = np.array([metrics[metric_key][n] for n in names])
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# Skip if all values are the same (no variance)
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if np.std(metric_values) == 0:
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print(f"\n{metric_label}: No variance, skipping")
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continue
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# Compute correlations
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pearson_r, pearson_p = stats.pearsonr(depths, metric_values)
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spearman_r, spearman_p = stats.spearmanr(depths, metric_values)
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# R-squared
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z = np.polyfit(depths, metric_values, 1)
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y_pred = np.polyval(z, depths)
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ss_res = np.sum((metric_values - y_pred) ** 2)
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ss_tot = np.sum((metric_values - np.mean(metric_values)) ** 2)
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r_squared = 1 - (ss_res / ss_tot) if ss_tot > 0 else 0
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results.append({
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'metric': metric_label,
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'key': metric_key,
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'pearson_r': pearson_r,
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'pearson_p': pearson_p,
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'spearman_r': spearman_r,
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'spearman_p': spearman_p,
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'r_squared': r_squared,
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'slope': z[0],
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'intercept': z[1],
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'values': metric_values
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})
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print(f"\n{metric_label}:")
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print(f" Pearson r = {pearson_r:.4f} (p = {pearson_p:.6f})")
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print(f" Spearman rho = {spearman_r:.4f} (p = {spearman_p:.6f})")
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print(f" R-squared = {r_squared:.4f}")
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# Sort by absolute Pearson correlation
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results.sort(key=lambda x: abs(x['pearson_r']), reverse=True)
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print("\n" + "=" * 80)
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print("SUMMARY: Metrics ranked by |Pearson r|")
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print("=" * 80)
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print(f"{'Metric':<25} {'Pearson r':>12} {'p-value':>12} {'Spearman':>12} {'R-squared':>12}")
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print("-" * 75)
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for r in results:
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sig = "*" if r['pearson_p'] < 0.05 else " "
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print(f"{r['metric']:<25} {r['pearson_r']:>11.4f}{sig} {r['pearson_p']:>12.6f} {r['spearman_r']:>12.4f} {r['r_squared']:>12.4f}")
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print("\n* = statistically significant at p < 0.05")
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# Create comparison plot (2x4 grid)
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fig, axes = plt.subplots(2, 4, figsize=(16, 8))
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axes = axes.flatten()
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for idx, r in enumerate(results):
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if idx >= 8:
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break
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ax = axes[idx]
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# Add jitter for visibility
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jitter = np.random.normal(0, 0.02 * np.std(r['values']), len(r['values']))
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ax.scatter(depths, r['values'] + jitter, alpha=0.7, s=60, c='steelblue', edgecolors='navy')
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# Trend line
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x_line = np.linspace(min(depths), max(depths), 100)
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y_line = r['slope'] * x_line + r['intercept']
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ax.plot(x_line, y_line, 'r--', alpha=0.8)
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ax.set_xlabel('Conceptual Depth', fontsize=10)
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ax.set_ylabel(r['metric'], fontsize=10)
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sig_marker = "*" if r['pearson_p'] < 0.05 else ""
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ax.set_title(f"r = {r['pearson_r']:.3f}{sig_marker}, R² = {r['r_squared']:.3f}", fontsize=10)
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ax.grid(True, alpha=0.3)
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# Hide unused subplots
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for idx in range(len(results), 8):
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axes[idx].set_visible(False)
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plt.suptitle('Conceptual Depth vs Graph Metrics (n=33 non-letter nodes)', fontsize=12, y=1.02)
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plt.tight_layout()
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plt.savefig(r'C:\Users\alexa\copycat\slipnet_analysis\centrality_comparison.png', dpi=150, bbox_inches='tight')
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print(f"\nComparison plot saved to: centrality_comparison.png")
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# Create individual detailed plots for top 4 metrics
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fig2, axes2 = plt.subplots(2, 2, figsize=(12, 10))
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axes2 = axes2.flatten()
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for idx, r in enumerate(results[:4]):
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ax = axes2[idx]
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jitter = np.random.normal(0, 0.02 * np.std(r['values']), len(r['values']))
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ax.scatter(depths, r['values'] + jitter, alpha=0.7, s=80, c='steelblue', edgecolors='navy')
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# Add labels
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for i, name in enumerate(names):
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ax.annotate(name, (depths[i], r['values'][i] + jitter[i]),
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fontsize=7, alpha=0.7, xytext=(3, 3), textcoords='offset points')
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# Trend line
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x_line = np.linspace(min(depths), max(depths), 100)
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y_line = r['slope'] * x_line + r['intercept']
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ax.plot(x_line, y_line, 'r--', alpha=0.8,
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label=f'y = {r["slope"]:.4f}x + {r["intercept"]:.4f}')
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ax.set_xlabel('Conceptual Depth', fontsize=11)
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ax.set_ylabel(r['metric'], fontsize=11)
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sig_text = " (significant)" if r['pearson_p'] < 0.05 else " (not significant)"
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ax.set_title(f"{r['metric']}\nPearson r = {r['pearson_r']:.3f} (p = {r['pearson_p']:.4f}){sig_text}",
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fontsize=11)
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ax.legend(loc='best', fontsize=9)
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ax.grid(True, alpha=0.3)
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plt.suptitle('Top 4 Metrics: Conceptual Depth Correlations', fontsize=13)
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plt.tight_layout()
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plt.savefig(r'C:\Users\alexa\copycat\slipnet_analysis\top_metrics_detailed.png', dpi=150, bbox_inches='tight')
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print(f"Detailed plot saved to: top_metrics_detailed.png")
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# Save results to JSON for paper
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output_data = {
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'analysis_type': 'centrality_correlation',
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'n_nodes': len(names),
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'metrics': []
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}
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for r in results:
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output_data['metrics'].append({
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'name': r['metric'],
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'key': r['key'],
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'pearson_r': round(r['pearson_r'], 4),
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'pearson_p': round(r['pearson_p'], 6),
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'spearman_r': round(r['spearman_r'], 4),
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'spearman_p': round(r['spearman_p'], 6),
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'r_squared': round(r['r_squared'], 4),
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'significant': bool(r['pearson_p'] < 0.05)
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})
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with open(r'C:\Users\alexa\copycat\slipnet_analysis\centrality_results.json', 'w') as f:
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json.dump(output_data, f, indent=2)
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print(f"Results saved to: centrality_results.json")
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# Print data table for paper
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print("\n" + "=" * 80)
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print("DATA TABLE FOR PAPER")
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print("=" * 80)
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print(f"{'Node':<25} {'Depth':>6} {'Degree':>8} {'Between':>8} {'Close':>8} {'Eigen':>8} {'PageRank':>8}")
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print("-" * 80)
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sorted_nodes = sorted(zip(names, depths), key=lambda x: x[1])
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for name, depth in sorted_nodes:
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deg = metrics['degree'][name]
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bet = metrics['betweenness'][name]
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clo = metrics['closeness'][name]
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eig = metrics['eigenvector'][name]
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pr = metrics['pagerank'][name]
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print(f"{name:<25} {depth:>6.0f} {deg:>8.4f} {bet:>8.4f} {clo:>8.4f} {eig:>8.4f} {pr:>8.4f}")
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if __name__ == '__main__':
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main()
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