IFN Lab: Power Dynamics
Core Concepts
Power = Influence an actor has over others in a network
Capacity Matrix = Input showing relationship strengths
Ideal Flow Matrix = Balanced power distribution (output)
Key Principles:
1. Irreducible
Networks must be strongly connected
Every point can reach
any other point by following links
2. Premagic
Ideal Flow = Balanced Power (∑ inflows = ∑ outflows)
Power is balanced when
what goes in equals what goes out
Incomplete Network
Incomplete networks create dictatorships (sources) or redundancies (sinks)
Leads to unchecked controllers (sources)
or removable elements (sinks)
Why Balance Matters: Without balanced power, influence concentrates, creating inefficiencies, unfair systems, or even system collapse.
Network Types
Premier Network
Minimal whole-number flows preserving connections
Focus: Structural relationships
Best for: Analyzing network topology
Uses the original network structure but may change some flow ratios.
It finds the smallest whole‐number flows that keep each node connected.
Think of it like finding a simplest 'prime' building block of flows.
Cardinal Network
Exact proportional scaling to strength of influences
Focus: Precision ratios
Best for: Real-world applications
Preserves the exact flow proportions (stochastic matrix) from the input.
It scales all fractions by the least common multiple so every flow is a whole number.
This one exactly matches the original ratios but can produce large values.
Comparison Insight: Premier focuses on network structure while Cardinal provides exact strength proportions as the input capacity matrix.
Explore how network structure shapes power using Ideal Flow Networks, signatures, and real-world examples.
Lab Instructions
1. Generate Matrix
Create random irreducible capacity matrix
2. Visualize Matrix
View relationship strengths
3. Analyze Properties
Check: Irreducible? Premagic? Ideal Flow? Symmetric?
4. Compute IFN
Transform to ideal flow matrix (choose network type)
5. Interpret Power Distribution
Observe power balance and the power of target node (customer in business, people in politics, building in construction)
Critical Step: Always ensure matrix is irreducible (i.e. strongly connected network) before computing ideal flow!
The IFN Power Dynamics Lab is an interactive virtual tool that lets you explore how influence shifts within a network by simulating changes in relationships using Ideal Flow Network analysis.
Key Experiments
Power Shift
Change one link strength → Observe power redistribution
- Strengthen a weak link: Does power concentrate?
- Weaken a strong link: Who gains influence?
Network Comparison
Run all network types → Note differences
- Which actors gain/lose power in each type?
- When would you use Premier vs. Cardinal?
Broken Systems
Given disconnected network → Check Irreducibility
- Add node which is the target of the system and form closed feedback loop by adding communication links to make strongly connected network
- Add minimum links to restore bidirectional communication
- Optionally create symmetric network structure
Centrality Explorer
Test all centrality types → Discover unique insights
- Which nodes are most influential in each measure?
- When do short-term vs. long-term influence matter?
Why Ideal Flow Matters
Ideal Flow Networks reveal hidden power structures that aren't apparent in raw capacity matrices, showing who truly influences whom when the system reaches equilibrium.
The principles of Ideal Flow Networks apply universally across systems. By understanding the core concepts, you can adapt IFN analysis to any context where power dynamics matter.
Universal Application Framework
Identify Your Actors
Who are the key players? Look for entities that can influence, communicate with, or control others. These could be people, departments, organizations, or even abstract concepts like "public opinion" or "market forces."
Consider the Factors
What drives the dynamics? Explore underlying elements—social, economic, technological—that shape outcomes or constraints. These can overlap with actors or stand alone as background forces.
Map the Relationships
How do they interact? Identify channels of influence, communication, authority, feedback, or resource flow. Consider both formal relationships (org charts, laws) and informal ones (networks, culture, trust).
Question the Balance
Who has too much or too little power? Look for concentration points that create bottlenecks, single points of failure, or marginalized voices that should have more influence.
Tweak the Structure
What if we changed the network? Try adding or removing nodes, or reconfiguring links between them. This alters how influence flows, who has access, and where new possibilities emerge.
Adjust Influence Strength
What if the same actors had more or less sway? Experiment with varying the intensity of relationships. The IFN helps you see how even subtle changes in influence reshape power dynamics.
Common Patterns Across Domains
Hierarchical Systems
Organizations, governments, families - where formal authority meets informal influence
Stakeholder Networks
Multi-party situations where different groups have competing interests but must collaborate
Market Dynamics
Economic systems where suppliers, consumers, regulators, and intermediaries interact
Communication Systems
Information flow networks where message control, filtering, and amplification matter
System Principle
Sustainable systems require checks and balances. Power must flow in accountable feedback loops — not concentrate — so no single entity can dominate without oversight. Every node must influence and be influenced, ensuring mutual regulation and preventing single-point control. Healthy networks avoid both dictatorships (source nodes that only output influence) and redundant dead ends (sink nodes that only receive influence). The Flow of Power must circulate — not concentrate — for long-term stability.
Examples Real-World Applications
Business
Balance power across departments and foster customer-centric innovation
Community Development
Ensure equitable resource distribution among stakeholders
Politics
Empower citizens and strengthen democratic checks and balances
Social Networks
Identify influencers, bridges, and echo chambers
Economics
Redistribute resources to reduce income inequality
Organizational Design
Create dynamic feedback systems for adaptive structures
Education
Shape student–teacher dynamics for inclusive learning environments
Urban Planning
Balance developer, government, and citizen influences
Disaster Response
Coordinate agencies and community voices in crises
Legal Systems
Ensuring fairness in judicial proceedings and reducing corruption
International Relations
Shape diplomatic alliances and power equilibria
Supply Chain Management
Optimize stakeholder influence for resilient logistics
Sports Teams
Align coach, player, and management dynamics for peak performance
Healthcare
Balance patient–provider authority to improve access and outcomes
Workplace
Negotiate salaries and benefits to empower employees
Social Movements
Understanding the rise and fall of movements based on power shifts
Artificial Intelligence
Balancing influence in AI ethics and governance
Environmental Policy
Balance corporate influence with ecological sustainability
Student Challenge
Model a 4-actor system (e.g., family members or project team):
- Define capacity matrix showing influence relationships
- Compute ideal flows using different network types (Premier/Cardinal)
- Answer: "Who holds the most power? How would you balance influence?"
Lab Tool: IFN Power Dynamics
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Input Capacity Matrix
Pattern of Capacity Matrix
Convert to IFN
Output Ideal Flow Matrix
Pattern of Ideal Flow Matrix