Network Analysis

Overview

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.

When to Use

• Analyzing social networks to identify influential users and community structures
• Mapping organizational hierarchies and identifying key connectors or bottlenecks
• Studying citation networks to find impactful research papers and collaboration patterns
• Building recommendation systems based on network relationships and similarities
• Analyzing supply chain networks to optimize logistics and identify vulnerabilities
• Detecting fraud patterns through network analysis of financial transactions

Network Concepts

• Nodes: Individual entities
• Edges: Connections/relationships
• Degree: Number of connections
• Centrality: Node importance measures
• Community: Densely connected groups
• Clustering Coefficient: Local density

Key Metrics

• Degree Centrality: Number of connections
• Betweenness Centrality: Control over paths
• Closeness Centrality: Average distance to others
• Eigenvector Centrality: Connections to important nodes
• Modularity: Community structure strength

Implementation with Python

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)