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 ) 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

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print

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"NETWORK ANALYSIS SUMMARY"

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f"Most influential:

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f"Most connected:

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f"Network bottleneck:

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print

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f"Closest to all:

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Centrality Measures

Degree

Direct connections only

Betweenness

Bridges between groups

Closeness

Access to network

Eigenvector

Connected to important nodes

PageRank

Random walk probability

Community Detection

Modularity Optimization

Find dense groups

Louvain Algorithm

Hierarchical communities

K-clique

Overlapping communities

Spectral

Eigenvalue-based Applications Social network analysis Organizational structures Citation networks Recommendation networks Supply chain analysis Deliverables Network visualization Centrality analysis Community detection results Connectivity metrics Influence rankings Key node identification Network statistics summary