Analyze network structures, identify communities, measure centrality, and visualize relationships for social networks and organizational structures
This skill enables analysis of network structures to identify communities, measure centrality, detect influential nodes, and visualize complex relationships in social networks, organizational structures, and interconnected systems.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import networkx as nx
from collections import defaultdict, Counter
import seaborn as sns
# Create sample network (social network)
G = nx.Graph()
# Add nodes with attributes
nodes = [
('Alice', {'role': 'Manager', 'dept': 'Sales'}),
('Bob', {'role': 'Engineer', 'dept': 'Tech'}),
('Carol', {'role': 'Designer', 'dept': 'Design'}),
('David', {'role': 'Engineer', 'dept': 'Tech'}),
('Eve', {'role': 'Analyst', 'dept': 'Sales'}),
('Frank', {'role': 'Manager', 'dept': 'HR'}),
('Grace', {'role': 'Designer', 'dept': 'Design'}),
('Henry', {'role': 'Engineer', 'dept': 'Tech'}),
('Iris', {'role': 'Analyst', 'dept': 'Sales'}),
('Jack', {'role': 'Manager', 'dept': 'Finance'}),
]
for node, attrs in nodes:
G.add_node(node, **attrs)
# Add edges (relationships)
edges = [
('Alice', 'Bob'), ('Alice', 'Carol'), ('Alice', 'Eve'),
('Bob', 'David'), ('Bob', 'Henry'), ('Carol', 'Grace'),
('David', 'Henry'), ('Eve', 'Iris'), ('Frank', 'Jack'),
('Grace', 'Carol'), ('Alice', 'Frank'), ('Bob', 'Carol'),
('Eve', 'Alice'), ('Iris', 'Eve'), ('Jack', 'Frank'),
('Henry', 'David'), ('Carol', 'David'),
]
G.add_edges_from(edges)
print("Network Summary:")
print(f"Nodes: {G.number_of_nodes()}")
print(f"Edges: {G.number_of_edges()}")
print(f"Density: {nx.density(G):.2%}")
# 1. Degree Centrality
degree_centrality = nx.degree_centrality(G)
print("\n1. Degree Centrality (Top 5):")
for node, score in sorted(degree_centrality.items(), key=lambda x: x[1], reverse=True)[:5]:
print(f" {node}: {score:.3f}")
# 2. Betweenness Centrality (control over network)
betweenness_centrality = nx.betweenness_centrality(G)
print("\n2. Betweenness Centrality (Top 5):")
for node, score in sorted(betweenness_centrality.items(), key=lambda x: x[1], reverse=True)[:5]:
print(f" {node}: {score:.3f}")
# 3. Closeness Centrality (average distance to others)
closeness_centrality = nx.closeness_centrality(G)
print("\n3. Closeness Centrality (Top 5):")
for node, score in sorted(closeness_centrality.items(), key=lambda x: x[1], reverse=True)[:5]:
print(f" {node}: {score:.3f}")
# 4. Eigenvector Centrality
try:
eigenvector_centrality = nx.eigenvector_centrality(G, max_iter=100)
print("\n4. Eigenvector Centrality (Top 5):")
for node, score in sorted(eigenvector_centrality.items(), key=lambda x: x[1], reverse=True)[:5]:
print(f" {node}: {score:.3f}")
except:
print("\n4. Eigenvector Centrality: Not converged")
# 5. Community Detection (using modularity)
from networkx.algorithms import community
communities = list(community.greedy_modularity_communities(G))
print(f"\n5. Community Detection:")
print(f"Number of communities: {len(communities)}")
for i, comm in enumerate(communities):
print(f" Community {i+1}: {list(comm)}")
# 6. Network Statistics
degrees = [G.degree(n) for n in G.nodes()]
print(f"\n6. Network Statistics:")
print(f"Average Degree: {np.mean(degrees):.2f}")
print(f"Max Degree: {max(degrees)}")
print(f"Min Degree: {min(degrees)}")
print(f"Clustering Coefficient: {nx.average_clustering(G):.3f}")
print(f"Number of Triangles: {sum(nx.triangles(G).values()) // 3}")
# Visualization
fig, axes = plt.subplots(2, 2, figsize=(15, 12))
# Network layout
pos = nx.spring_layout(G, k=0.5, iterations=50, seed=42)
# 1. Network Graph (colored by degree)
ax = axes[0, 0]
node_colors = [degree_centrality[node] for node in G.nodes()]
nx.draw_networkx_nodes(G, pos, node_color=node_colors, node_size=1000, cmap='YlOrRd', ax=ax)
nx.draw_networkx_edges(G, pos, alpha=0.5, ax=ax)
nx.draw_networkx_labels(G, pos, font_size=8, ax=ax)
ax.set_title('Network Graph (Colored by Degree Centrality)')
ax.axis('off')
# 2. Network Graph (colored by communities)
ax = axes[0, 1]
color_map = []
colors = plt.cm.Set3(np.linspace(0, 1, len(communities)))
node_to_color = {}
for i, comm in enumerate(communities):
for node in comm:
node_to_color[node] = colors[i]
color_map = [node_to_color[node] for node in G.nodes()]
nx.draw_networkx_nodes(G, pos, node_color=color_map, node_size=1000, ax=ax)
nx.draw_networkx_edges(G, pos, alpha=0.5, ax=ax)
nx.draw_networkx_labels(G, pos, font_size=8, ax=ax)
ax.set_title('Network Graph (Colored by Community)')
ax.axis('off')
# 3. Centrality Comparison
ax = axes[1, 0]
centrality_df = pd.DataFrame({
'Degree': degree_centrality,
'Betweenness': betweenness_centrality,
'Closeness': closeness_centrality,
}).head(8)
centrality_df.plot(kind='barh', ax=ax, width=0.8)
ax.set_xlabel('Centrality Score')
ax.set_title('Top 8 Nodes - Centrality Comparison')
ax.legend(loc='lower right')
ax.grid(True, alpha=0.3, axis='x')
# 4. Degree Distribution
ax = axes[1, 1]
degree_sequence = sorted([d for n, d in G.degree()], reverse=True)
degree_count = Counter(degree_sequence)
degrees_unique = sorted(degree_count.keys())
counts = [degree_count[d] for d in degrees_unique]
ax.bar(degrees_unique, counts, color='steelblue', edgecolor='black', alpha=0.7)
ax.set_xlabel('Degree')
ax.set_ylabel('Count')
ax.set_title('Degree Distribution')
ax.grid(True, alpha=0.3, axis='y')
plt.tight_layout()
plt.show()
# 7. Path Analysis
print(f"\n7. Path Analysis:")
try:
shortest_path = nx.shortest_path_length(G, 'Alice', 'Jack')
print(f"Shortest path from Alice to Jack: {shortest_path}")
except nx.NetworkXNoPath:
print("No path exists between nodes")
# 8. Connectivity Analysis
print(f"\n8. Connectivity Analysis:")
print(f"Is connected: {nx.is_connected(G)}")
num_components = nx.number_connected_components(G)
print(f"Number of connected components: {num_components}")
# 9. Similarity Measures
def jaccard_similarity(node1, node2):
neighbors1 = set(G.neighbors(node1)) | {node1}
neighbors2 = set(G.neighbors(node2)) | {node2}
intersection = len(neighbors1 & neighbors2)
union = len(neighbors1 | neighbors2)
return intersection / union if union > 0 else 0
print(f"\n9. Node Similarity (Jaccard):")
print(f"Alice & Bob: {jaccard_similarity('Alice', 'Bob'):.3f}")
print(f"Alice & Jack: {jaccard_similarity('Alice', 'Jack'):.3f}")
# 10. Influence Score (Combination of metrics)
influence_score = {}
for node in G.nodes():
score = (degree_centrality[node] * 0.4 +
betweenness_centrality[node] * 0.3 +
closeness_centrality[node] * 0.3)
influence_score[node] = score
print(f"\n10. Influence Score (Top 5):")
for node, score in sorted(influence_score.items(), key=lambda x: x[1], reverse=True)[:5]:
print(f" {node}: {score:.3f}")
# Summary
print("\n" + "="*50)
print("NETWORK ANALYSIS SUMMARY")
print("="*50)
print(f"Most influential: {max(influence_score, key=influence_score.get)}")
print(f"Most connected: {max(degree_centrality, key=degree_centrality.get)}")
print(f"Network bottleneck: {max(betweenness_centrality, key=betweenness_centrality.get)}")
print(f"Closest to all: {max(closeness_centrality, key=closeness_centrality.get)}")
print("="*50)
