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Motif Z-Score Explorer

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About This MicroSim

A subgraph pattern becomes a network motif not simply by occurring frequently, but by occurring significantly more often than expected in a random network with the same degree sequence. The Z-score measures this significance: \(Z = (\text{count}_\text{real} - \mu_\text{random}) / \sigma_\text{random}\).

This MicroSim computes Z-scores for wedge, triangle, 4-path, 4-star, and 4-cycle patterns on a network you choose. The bar chart at the bottom shows Z-scores alongside raw counts, making the difference between "common" and "significant" visible.

Learning objective (Bloom's Analyze (Level 4)): Distinguish network motifs (statistically over-represented subgraphs, \(Z > 2\)) from anti-motifs (under-represented, \(Z < -2\)) vs. raw frequency, and see how the null model matters.

How to Use

  1. Choose a network — load a preset (regulatory network, social network, random graph).
  2. Read the Z-scores — the bar chart shows Z-scores for each subgraph pattern. Red bars indicate motifs (Z > 2); blue bars indicate anti-motifs (Z < −2).
  3. Compare raw counts — toggle "Show Raw Counts" to compare Z-scores to absolute frequencies.
  4. Null model — choose between degree-preserving random rewiring and Erdős–Rényi null models.
  5. Hover a pattern icon — see the pattern definition and example occurrence in the loaded network.

Iframe Embed Code

You can embed this MicroSim in any web page with the following HTML:

<iframe src="https://AnvithPothula.github.io/graph-neural-networks-textbook/sims/ch19-motif-zscore/main.html"
        height="522"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

Undergraduate / Graduate (College Level)

Duration

20–30 minutes

Prerequisites

Subgraphs and graphlets (Chapter 19 intro). Z-score and statistical significance. Null models.

Activities

  1. Load the regulatory network. Which pattern has the highest Z-score? Why is this pattern functionally important in gene regulation?
  2. Load a random Erdős–Rényi graph. All Z-scores should hover near zero. Verify this.
  3. Switch the null model from degree-preserving to Erdős–Rényi on the same network. How do the Z-scores change? Which null model is more conservative?

Assessment Question

Define a network motif formally using statistical significance. Explain why a feed-forward loop is a motif in transcriptional regulation but not in a social network.

References

  1. Milo et al. (2002). Network Motifs: Simple Building Blocks of Complex Networks. Science.
  2. Przulj (2007). Biological network comparison using graphlet degree distribution. Bioinformatics.

Part of Chapter 19: Frequent Subgraph Mining. Return to the chapter page or browse all MicroSims.