graph-thinking

• Mapping feature dependencies in product development
• Analyzing stakeholder relationships
• Understanding system architectures
• Exploring interconnected concepts
• Designing recommendation systems or knowledge graphs
• Identifying opportunity areas through network analysis

Graph Elements

| Element | Description |

| -------------- | ------------------------------------------ |

| Nodes | Individual elements or concepts |

| Edges | Relationships or connections between nodes |

| Clusters | Groups of highly connected nodes |

| Pathways | Routes through the network |

| Centrality | Measures identifying most important nodes |

| Topology | Structural arrangement of connections |

Graph-of-Thought (GoT) Reasoning

```

Traditional (Chain-of-Thought):

A → B → C → D → Conclusion

Graph-of-Thought:

┌─── B ───┐

│ │

A ──┼─── C ───┼──→ Synthesis → Conclusion

│ │

└─── D ───┘

↑

Feedback Loop

```

GoT enables:

• Combining arbitrary thoughts into synergistic outcomes
• Distilling networks of thoughts for clarity
• Enhancing ideas using feedback loops
• Non-linear exploration of solution spaces

First Principles Thinking

Break down complex problems into fundamental truths:

```

Surface Level:

"We need more marketing"

↓

Why?

↓

"Not enough customers"

↓

Why?

↓

Root Truth:

"Value proposition unclear to target audience"

```

Second-Order Thinking

Demand deeper analysis by asking "And then what?":

```

Decision: Reduce prices by 20%

First-order: More sales

Second-order: Lower margins → Less R&D budget

Third-order: Competitors catch up → Price war

Fourth-order: Race to bottom → Industry commoditization

```

Non-Linear Processing

Unlike sequential thinking:

| Sequential | Graph-Based |

| ----------------------- | ----------------------------------------- |

| One path at a time | Multiple paths simultaneously |

| Linear information flow | Multi-directional exploration |

| Fixed order | Iterative refinement through loops |

| Single conclusion | Synthesized insights from multiple angles |

Double Diamond Model

Apply divergent and convergent thinking cycles:

```

DISCOVER DEFINE DEVELOP DELIVER

(Diverge) (Converge) (Diverge) (Converge)

/\ \/ /\ \/

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

Explore Focus on Generate Focus on

problem specific diverse optimal

space challenges solutions implementation

```

Step 1: Map the Nodes

Identify all relevant elements:

```

Product Launch Analysis:

Nodes:

├── Stakeholders

│ ├── Customers

│ ├── Engineering

│ ├── Marketing

│ └── Leadership

├── Features

│ ├── Core functionality

│ ├── Nice-to-haves

│ └── Technical debt

├── Constraints

│ ├── Timeline

│ ├── Budget

│ └── Resources

└── Dependencies

├── External APIs

├── Infrastructure

└── Regulatory

```

Step 2: Define Relationships (Edges)

Document connections between nodes:

```

Edge Types:

├── Dependency: A requires B

├── Influence: A affects B

├── Correlation: A and B move together

├── Conflict: A competes with B

└── Synergy: A enhances B

```

Step 3: Identify Clusters and Patterns

Find highly connected groups:

```

High Centrality (Critical Nodes):

├── Authentication service → 12 dependencies

├── Database layer → 8 dependencies

└── API gateway → 6 dependencies

Clusters:

├── User-facing features (tightly coupled)

├── Backend services (loosely coupled)

└── Third-party integrations (isolated)

```

Step 4: Analyze Pathways

Trace routes through the network:

```

User Journey Graph:

Landing Page

↓

[Sign Up] ←→ [Social Login]

↓

Onboarding

↓ ↓

Quick Start Full Setup

↓ ↓

└─────┬─────┘

↓

First Value

↓

↙ ↓ ↘

Churn Retain Upgrade

```

After completing analysis, document as:

```markdown

Subject: [What you're analyzing]

Analysis Date: [Date]

Node Map

| Category | Nodes | Centrality |

| -------- | ------- | -------------- |

| [Cat 1] | [Nodes] | [High/Med/Low] |

| [Cat 2] | [Nodes] | [High/Med/Low] |

Relationship Matrix

| From | To | Relationship | Strength |

| ---- | --- | ------------ | -------- |

| [A] | [B] | [Type] | [1-5] |

Key Insights

1. Clusters identified: [Description]
2. Critical paths: [Description]
3. Bottlenecks: [Description]
4. Opportunities: [Description]

Recommendations

| Priority | Action | Rationale |

| -------- | -------- | --------- |

| High | [Action] | [Why] |

| Medium | [Action] | [Why] |

```

Feature Dependency Mapping

```

Feature: Real-time Collaboration

Dependencies:

├── WebSocket infrastructure

│ ├── Connection management

│ └── Message queuing

├── Conflict resolution

│ ├── Operational transforms

│ └── CRDT implementation

├── Presence indicators

│ └── User state sync

└── Permissions

├── Document access

└── Cursor visibility

```

Stakeholder Analysis

```

HIGH INFLUENCE

│

Keep Satisfied │ Manage Closely

┌─────────────────────┼─────────────────────┐

│ │ │

│ Executives │ Product Owner │

│ Compliance │ Key Customers │

│ │ │

LOW ──────────────────────┼────────────────────── HIGH

INTEREST │ INTEREST

│ │ │

│ General Users │ Power Users │

│ IT Support │ Dev Team │

│ │ │

└─────────────────────┼─────────────────────┘

Monitor │ Keep Informed

│

LOW INFLUENCE

```

System Architecture Analysis

```

Microservice Graph:

API Gateway [Centrality: 0.95]

│

├── Auth Service [0.82]

│ └── User DB

│

├── Product Service [0.71]

│ ├── Catalog DB

│ └── Search Index

│

├── Order Service [0.68]

│ ├── Order DB

│ └── Payment Gateway (external)

│

└── Notification Service [0.45]

└── Email Provider (external)

Critical Path: Gateway → Auth → Product → Order

Bottleneck: Auth Service (single point of failure)

```

Do

• Visualize relationships - Draw the graph, don't just describe it
• Iterate continuously - Graphs evolve as understanding deepens
• Measure centrality - Identify the most critical nodes
• Look for clusters - Natural groupings reveal system structure
• Trace pathways - Understand how information/value flows

Avoid

• Over-connecting - Not everything relates to everything
• Ignoring edge types - Different relationships have different meanings
• Static thinking - Graphs change over time
• Missing feedback loops - Circular dependencies are significant
• Forgetting weights - Some relationships are stronger than others

| Method | Combined Use |

| ------------------- | ---------------------------------------------- |

| Five Whys | Trace causal chains through the graph |

| Business Canvas | Map relationships between canvas elements |

| Jobs-to-be-Done | Connect user needs to feature nodes |

| Hypothesis Tree | Structure experiments as branching graphs |

| Stakeholder Map | Visualize influence and interest relationships |

Visualization

• Mermaid - Code-based diagrams in markdown
• Graphviz - Programmatic graph generation
• Excalidraw - Hand-drawn style diagrams
• Miro/FigJam - Collaborative whiteboarding

Analysis

• Gephi - Network analysis and visualization
• Neo4j - Graph database for complex queries
• NetworkX - Python library for graph algorithms

• [Graph of Thoughts: ArXiv Paper](https://arxiv.org/abs/2308.09687)
• [Neo4j Graph Database Use Cases](https://neo4j.com/use-cases/)
• [Network Science by Albert-László Barabási](http://networksciencebook.com/)