Hierarchical network analysis with graph traversal algorithms and performance optimization metrics for complex data structures.
This system implements advanced graph algorithms for analyzing hierarchical networks and tree-like data structures. Using breadth-first search, depth-first search, and network topology analysis, the system computes structural metrics, identifies optimization opportunities, and generates comprehensive visualizations for decision support and performance analysis.
- Graph Traversal Algorithms: BFS and DFS implementations for shortest path and exhaustive search
- Topological Analysis: Root identification and hierarchical structure validation
- Performance Metrics: Branching factor analysis, depth distribution, and connectivity measurement
- Path Optimization: Complete path enumeration with statistical analysis
- Network Visualization: Color-coded hierarchical layouts with NetworkX integration
- Data Format Flexibility: Support for CSV, tab-delimited, and space-separated input formats
Graph Theory Algorithms:
- Breadth-First Search: Shortest path computation from root to any node
- Depth-First Search: Complete path enumeration for terminal node analysis
- Topological Sorting: Root node identification in directed acyclic graphs
Performance Metrics:
- Branching Factor: Average and maximum child node count per internal node
- Depth Analysis: Maximum and average path lengths from root to terminals
- Connectivity Metrics: Edge density and structural complexity measures
State Transition Analysis:
- Dimensional Change Tracking: Frequency analysis of state vector modifications
- Transition Pattern Recognition: Systematic analysis of node transformation patterns
- System Architecture Analysis: Hierarchical system performance optimization
- Decision Tree Evaluation: Complex decision structure analysis and simplification
- Network Topology Assessment: Communication network efficiency analysis
- Algorithm Performance Testing: Comparative analysis of traversal methods
# Load hierarchical data structure
graph = load_hierarchical_data('network_data.txt')
# Perform comprehensive structural analysis
graph.analyze_structure()
# Generate network visualization
graph.visualize_network('analysis_output.png')
# Execute advanced path analysis
compute_path_analysis(graph)python graph_analysis.pyThe system accepts hierarchical relationships in multiple formats:
# CSV format
"(1,2,3)","(1,2,4)"
"(1,2,4)","(1,3,4)"
# Tab-delimited format
(1,2,3) (1,2,4)
(1,2,4) (1,3,4)
# Space-delimited format
(1,2,3) (1,2,4)
(1,2,4) (1,3,4)
project/
├── network_data.txt # Input hierarchical relationship data
├── graph_analysis.py # Main analysis implementation
├── .gitignore # Version control configuration
└── README.md # Project documentation
matplotlib>=3.5.0
networkx>=2.6
numpy>=1.21.0 # For advanced numerical operations- Clone repository:
git clone https://github.com/BigCatSoftware/graph-algorithm-analysis.git
cd graph-algorithm-analysis- Install dependencies:
pip install matplotlib networkx numpy- Run analysis:
python graph_analysis.pyThe system will process network_data.txt and generate comprehensive analysis output including network visualizations.
The system generates detailed reports including:
- Network Size: Total node and edge counts
- Depth Distribution: Maximum depth and average path lengths
- Branching Patterns: Average branching factor and structural complexity
- Terminal Analysis: Count and distribution of leaf nodes
- Complete Path Enumeration: All root-to-terminal paths
- Statistical Summary: Path length distribution and optimization metrics
- Transition Analysis: State vector change frequency and patterns
- Hierarchical Layout: Color-coded network structure (Red=Root, Green=Terminal, Blue=Internal)
- High-Resolution Export: 300 DPI network diagrams for professional presentation
- Scalable Display: Automatic label management for networks of varying complexity
Algorithmic Complexity:
- BFS Traversal: O(V + E) for shortest path computation
- DFS Enumeration: O(V + E) for complete path extraction
- Visualization: O(V²) for layout optimization with NetworkX
Memory Efficiency:
- Graph Storage: Adjacency list representation for sparse networks
- Path Caching: Optimized memory usage for large-scale analysis
- Incremental Processing: Streaming analysis for memory-constrained environments
- Visualization Thresholds: Automatic label hiding for networks >30 nodes
- Path Display Limits: Configurable sample path count for large networks
- Output Resolution: Customizable DPI settings for publication-quality graphics
- Format Detection: Automatic delimiter recognition for flexible input parsing
- Error Handling: Robust parsing with detailed error reporting
- Header Recognition: Automatic header row detection and skipping
Core Algorithm Classes:
HierarchicalGraph: Main graph data structure with traversal methodsload_hierarchical_data(): Multi-format data parser with error handlingcompute_path_analysis(): Statistical path enumeration and analysisanalyze_state_transitions(): Dimensional change pattern recognition
Visualization Pipeline:
- NetworkX integration for professional graph layouts
- Matplotlib rendering with customizable styling and color schemes
- Automatic node positioning using spring-force algorithms
- Export capabilities for multiple image formats
System Performance Analysis:
- Hierarchical system bottleneck identification
- Communication network optimization
- Decision tree pruning and simplification
Algorithm Validation:
- Comparative traversal method analysis
- Performance metric validation for optimization algorithms
- Structural complexity assessment for system design
- Directed Acyclic Graphs Only: System assumes hierarchical structure without cycles
- Memory Scaling: Large networks (>10,000 nodes) may require memory optimization
- Visualization Complexity: Dense networks may produce cluttered visual output
- Input Format Dependency: Requires structured tuple-based node representation
This project is available under the MIT License.