Complexity Analysis

Analyze architectural complexity using the Kauffman NK model and coupling matrix

The Complexity Analysis page helps you understand and measure the complexity of your software architecture using the Kauffman NK model --- a formal framework for analyzing system coupling and interdependencies.

Accessing Complexity Analysis

From your project navigation, click Architecture → Complexity to open the Complexity Analysis page.

NK Model Analysis

Archflow uses the Kauffman NK model to analyze architectural coupling. In this model:

N represents the number of systems in your architecture
K represents the average number of dependencies per system

Higher K values indicate tighter coupling, which increases complexity and makes the architecture harder to change.

Coupling Matrix

The coupling matrix is a visual grid showing system-to-system dependencies:

Each cell represents the coupling strength between two systems
Color-coded from low (green) to high (red) coupling
Diagonal represents self-coupling (internal complexity)
Helps identify clusters of tightly coupled systems

System Coupling Analysis

For each system, the analysis provides:

Coupling score --- Overall coupling metric based on connections
Fan-in --- Number of systems that depend on this system
Fan-out --- Number of systems this system depends on
Coupling type --- Afferent (incoming), efferent (outgoing), or balanced

High-Coupled Systems

The analysis automatically identifies systems with unusually high coupling:

Systems with far more connections than average
Hub systems that many others depend on
Systems with both high fan-in and fan-out (potential bottlenecks)

Complexity Metrics

The analysis also evaluates your architecture across traditional dimensions:

Connection Complexity

Total connections between systems
Average connections per system --- helps identify over-coupled or under-connected systems
Connection density --- ratio of actual connections to possible connections

Hierarchy Depth

Nesting levels --- how deep your system hierarchy goes
Child count distribution --- how many children each parent system has
Balance assessment --- whether the hierarchy is evenly distributed

System Distribution

Systems by type --- breakdown of Persons, Software Systems, Containers, and Components
Systems per level --- distribution across hierarchy levels

Interpreting Results

Well-Structured Architecture

A well-structured architecture typically shows:

Moderate connection density (not too sparse, not too dense)
Balanced hierarchy with consistent nesting depth
Clear separation between different system types
Low to moderate K values in the NK model

Warning Signs

Watch for these indicators of architectural issues:

Hub systems --- Systems with far more connections than average may be doing too much
Isolated systems --- Systems with zero connections may be missing relationships
Deep nesting --- Excessive hierarchy depth may indicate over-decomposition
High coupling clusters --- Groups of tightly coupled systems that should be refactored