qrWhatIFN

IFN Lab: Power Dynamics

By Kardi Teknomo, PhD
iFN

< Previous | Index | Next >

Brief Description

Power dynamics in networks refers to how influence or control is distributed among actors (people, organizations, etc.) or factors based on their connections and interactions. Based on Ideal Flow Network (IFN) analysis, we can explore how the strength of relationships between actors/factors affects their overall power within a network. This virtual lab helps you explore power dynamics in a network of actors (or factors). In this context, power means how much influence each actor (or factor) has over the others.

The network is built from a capacity matrix to represent these relationships. Each cell in the matrix shows the strength of influence one actor has on another. By converting this capacity matrix into an ideal flow matrix, we can analyze how power flows through the network and how it changes when connections or strengths are adjusted. From the capacity matrix, the lab computes an ideal flow matrix. This matrix shows balanced flows of influence so that, for every actor, the total power sent out equals the total power received. By looking at row sums in the ideal flow matrix, you see which actors hold more influence.

You can simulate change the capacity values, in both strength of influence and network structure. Then, you can observe how the ideal flow matrix updates. This way, you learn how small changes in relationships can shift power balances. The lab also shows different network types of integer IFNs (Premier, Cardinal) to compare how each method preserves or approximates the ideal flow.

Network Types: Premier or Cardinal

Premier Network: 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: 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.

Learning Objectives

Instruction

  1. Generate Random Capacity Matrix: Click the orange dice icon Random Capacity Matrix to create a random irreducible capacity matrix. Each row and column represents an actor.
  2. Visualize the Matrix: Click the heatmap icon Matrix Visualization to see the capacity matrix as colored cells. Darker colors mean stronger influence.
  3. Choose an Operation on the Capacity Matrix:
  4. Compute Ideal Flow Network: Select the network type (Premier, or Cardinal) from the dropdown. Then click the arrow icon Compute IFN to convert the capacity matrix into the ideal flow matrix.
  5. Work with Files:
    • To save the current matrix, click the CSV icon Save to CSV.
    • To load a saved CSV file, click the load icon Load from CSV and pick your file. The contents will appear in the text area.
  6. Visualize the Ideal Flow Matrix: After computing, click the heatmap icon next to the output area to see the ideal flow matrix as colors.
  7. Check Matrix Properties: For the ideal flow matrix, you can select operations like:
    • Is Irreducible?
    • Is Premagic?
    • Is Stochastic?
    • Is Ideal Flow?
    • Get Sum of Rows / Columns
    • And more…
  8. Visualize the Network Graph: Click the network icon Draw Network to redraw the network from the ideal flow matrix. Use the zoom icons Zoom In Zoom Out Reset Zoom to adjust the view.
  9. Get Help: Click the help icon Help to see instructions at any time.

Experiment and Discussion

  1. Create Your Own Scenario:
    • Think of a real-world situation with actors or factors (e.g., departments in a company, friends in a social circle).
    • Define who influences whom and how strongly. Write this as a capacity matrix in the text area or save a CSV file.
    • Compute the ideal flow matrix and note the row sums and column sums. Higher sums mean more overall influence (power).
  2. Compare Network Types:
    • Switch between Premier, and Cardinal networks. Compute each one and compare their ideal flow matrices.
    • Ask: How does each method keep or change the original influence strengths? Which actors gain or lose power?
  3. Investigate Matrix Properties:
    • Check if your capacity matrix is irreducible (all actors are connected). If not, try setting it to network structure to force connectivity.
    • Check if it is premagic (row sums = column sums). If it isn’t, you can convert it to be premagic.
    • Find the row stochastic matrix (rows sum to 1 or columns sum to 1). Compare the stochastic matrix of the capacity matrix and the ideal flow matrix. Are they the same? Which type of ideal flow networks that preserve the stochastic matrix of the capacity matrix input?
    • Once you have an ideal flow matrix, verify that it is balanced (sum of each row = sum of each column).
  4. Power Dynamics Challenge:
    • Take two capacity matrices that differ by only one or two links. Compare their ideal flow matrices to see how small changes shift power.
    • Try making a reducible matrix (disconnected group). Compute its ideal flow and you will see that it is not possible to ideal flow network from reducible network.
    • Convert your capacity matrix into a row-stochastic matrix (each row sums to 1). Compare this with the ideal flow’s stochastic matrix. What happens to each actor’s power share?

Lab Tool: IFN Power Dynamics

Capacity Matrix




Pattern of Capacity Matrix


Select Network Type:

Ideal Flow Matrix




Pattern of Ideal Flow Matrix

Ideal Flow Network

IFN Lab: IFN Power Dynamics

Index