Taxonomy of Network Analysis Indicators

Macro, Meso, and Node-Level Measures

SMM638 Network Analytics

Three Levels of Analysis

Network indicators operate at different scales:

Level	Focus	Questions
Macro	Entire network	How big? How centralized? How connected?
Meso	Groups/Communities	Are there clusters of nodes? How modular?
Micro/Node	Individual positions	Who is central? Who bridges groups?

Caution

Key Principle: Different levels reveal different insights

• Macro: Overall structure and properties
• Meso: Subgroup organization
  
• Micro: Individual advantages and constraints

Macro-Level Indicators

Whole Network Properties

Characterize the overall structure and global patterns

Key Measures:

1. Network Size: Number of nodes and edges
2. Density: Proportion of possible connections realized
3. Centralization: Concentration of connections
   
4. Diameter: Maximum distance between any two nodes
5. Average Path Length: Mean distance across all pairs
6. Fragmentation: Presence of disconnected components

Purpose: Understand network-wide characteristics and compare across networks

Example: Network Size and Density

Definition: Basic structural properties

• Node count: Total number of vertices (\(n\))
• Edge count: Total number of connections (\(m\))
• Possible edges: \(\frac{n(n-1)}{2}\) for undirected networks

Business Example: LinkedIn Network

• Small startup network (50 employees)
  • Possible connections: 1,225
  • Observed connections: 245
  • Density: 20%
• Large corporation network (5,000 employees)
  • Possible connections: 12,497,500
  • Observed connections: 187,500
  • Density: 1.5%

Insight: Larger networks typically have lower density

Network Metrics:

Nodes (n)	5
Edges (m)	6
Possible Edges	10
Density	60.0%

Example: Centralization

Definition: Extent to which connections concentrate around few nodes

• High centralization: Star-like, hierarchical structure
• Low centralization: Distributed, egalitarian structure

Business Example: Communication Patterns

Startup (Low Centralization = 0.25)

• Flat structure with distributed communication
• Multiple people coordinate projects
• Information flows through many channels

Traditional Corporation (High Centralization = 0.78)

• Hub-and-spoke: most communication through managers
• Clear hierarchy and formal reporting
• Information bottlenecks at central nodes

Implication: Centralization affects agility, innovation, and resilience

Network Metrics:

Network	Size	Density
Higher centralization (top)	5 nodes, 4 edges	40.0%
Lower centralization (bottom)	5 nodes, 8 edges	80.0%

Meso-Level Indicators

Community and Subgroup Structure

Identify cohesive groups and organizational patterns

Key Measures:

1. Modularity: Quality of network partitioning into groups
2. Community Detection: Algorithmic identification of clusters
3. Core-Periphery: Distinction between dense core and sparse periphery
4. Structural Holes: Gaps between groups creating brokerage opportunities
5. k-cores: Subgraphs where all nodes have minimum degree k

Purpose: Reveal hidden organizational structure and group boundaries

Example: Network Modularity

Definition: Strength of division into communities

• Measures how well network separates into distinct groups
• Higher values indicate stronger community structure

Business Example: Corporate R&D Network

Higher Modularity

• Clear separation: Chemistry, Biology, Engineering teams
• Limited cross-disciplinary collaboration
• Potential for siloed innovation

Lower Modularity

• Extensive cross-team connections
• Interdisciplinary collaboration
• Potential for breakthrough innovation but coordination challenges

Strategic Implication: Community structure reflects organizational integration vs. specialization trade-offs

Note

The top network seems to have two communities ({A, B, C} and {D, E, F} triads)

The bottom network does not show any obvious community structure

We will explore modularity indicators and community detection algorithms in detail in Weeks 7 and 8.

Node-Level Indicators

Individual Position and Influence

Characterize actor positions within the network

Major Categories:

1. Centrality Measures: Various ways to measure importance

   • Degree, Closeness, Betweenness, Eigenvector

2. Structural Position: Role in network architecture

   • Bridges, Brokers, Isolates, Cliques

3. Local Clustering: Cohesion of immediate neighborhood

4. Embeddedness: Integration into network structure

Purpose: Identify influential actors, structural advantages, and vulnerabilities

Note

Much more to follow on node-level indicators today

Summary: Levels in Practice

Integrated Analysis Framework:

Macro Level → Strategic organizational design

• Should we have a centralized or distributed structure?
• How connected is our organization overall?

Meso Level → Team and department dynamics

• Are we too siloed or too integrated?
• Where are the boundaries between groups?

Micro Level → Individual talent management

• Who are our key connectors and influencers?
• Who has structural advantages or disadvantages?

Important

Best Practice: Analyze networks at multiple levels simultaneously for comprehensive insights