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H01 electron microscopy with object segmentation and original 2 µm scale bar Nanoscale · Module 10

Network Science and Graph Representation

Teaching Deck

Human cortex · H01
Object segmentation over electron microscopy

H01 release · Lichtman Lab / Harvard & Connectomics at Google · CC BY 4.0
Shapson-Coe et al. (2024) · doi:10.1126/science.adk4858

Module 10 · Nanoscale

Learning Objectives

  • Construct graph representations from connectomics data
  • Compute and interpret core network metrics
  • Choose graph abstractions appropriate to specific hypotheses
  • Report assumptions and limits of graph-level conclusions
Module 10 · Nanoscale

Capability Target

Build one connectome graph representation and justify two metric choices for a defined hypothesis.

Module 10 · Nanoscale

Concept Focus

1) From EM to graph: a lossy transformation

A connectome graph is an abstraction. The path from EM images to a graph involves: raw images → segmentation → synapse detection → neuron-to-neuron edge list → graph. Each step loses information: the graph retains connectivity topology but discards spatial relationships, organelle details, and membrane geometry. This is a feature (graphs are computationally efficient and analytically tractable) and a limitation (the graph cannot answer questions that require spatial context).

Module 10 · Nanoscale

Core Workflow

  • Define node/edge schema: what are your nodes, what are your edges, what weighting scheme?
  • Construct graph from synapse table (e.g., using CAVEclient + NetworkX). Inspect: number of nodes, edges, density, connected components.
  • Compute candidate metrics: degree distribution, clustering, path length, reciprocity, modularity.
  • Compare each metric to null-model expectation (degree-preserving random graph as minimum).
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Core Workflow (continued)

  • Interpret metrics against hypothesis. Report which metrics are significant and which are not.
  • Document abstraction limits: what information was lost in the graph construction?
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Run of Show (60 min)

  • 00:00-08:00 | Graph abstraction choices
  • 08:00-20:00 | Graph build demo
  • 20:00-34:00 | Metric computation
  • 34:00-46:00 | Interpretation and null concerns
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Run of Show (60 min) (continued)

  • 46:00-60:00 | Competency check
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Misconceptions to Watch

  • Misconception guardrail: the connectivity graph is the data, rather than one lossy projection of it that discards all geometry.
  • Misconception guardrail: the synapse threshold is a technical detail that does not need reporting.
  • Misconception guardrail: a graph metric means the same thing biologically as it does in its original network-science context.
  • Misconception guardrail: Erdos-Renyi is an acceptable null for a spatially embedded, degree-heterogeneous connectome.
Module 10 · Nanoscale

Studio Activity

Scenario: You have the connectivity graph of 500 neurons in a cortical column from the MICrONS dataset. Your PI asks: "Is this circuit small-world? Are there hub neurons? Are there communities?"

Module 10 · Nanoscale

Activity Output Checklist

  • Evidence-linked artifact submitted.
  • At least one limitation or uncertainty stated.
  • Revision point captured from feedback.
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Assessment Rubric

Minimum pass

  • The node/edge schema is stated explicitly — node definition, edge direction, weighting, and synapse threshold — before any metric appears.
  • Each reported metric is paired with a null-model comparison; no bare metric values stand alone.
  • At least two metrics are linked in writing to the specific question they answer for the PI's three asks (small-world, hubs, communities).
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Assessment Rubric (continued)

  • The report names at least one piece of information the graph abstraction discarded and one question it therefore cannot answer.
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Assessment Rubric

Strong performance

  • The headline result is re-run at a second synapse threshold, and the report states which conclusions held and which moved.
  • Degree outliers are checked against the underlying reconstruction before being reported as hubs, with the check documented.
  • More than one null model is used, or the limits of the single null are stated in words (what it does and does not control for).
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Assessment Rubric (continued)

  • Detected communities are compared against external labels (cell types), and disagreement is reported as a finding rather than suppressed.
Module 10 · Nanoscale

Assessment Rubric

Common failure to flag

  • Metric dumping — computing every available metric without explaining what question each answers.
  • Hub or community claims made without checking whether a merge error or threshold choice manufactured them.
  • A significance claim against Erdos-Renyi only, on a graph with obvious degree heterogeneity.
Module 10 · Nanoscale

Exit Ticket

State one reason a graph metric might be misleading in your current dataset.

Module 10 · Nanoscale

References (Instructor)

  • Use module references listed on the module page.
Module 10 · Nanoscale

Teaching Materials

  • Module page: /modules/module10/
  • Session kit: /teaching/sessions/module10/
  • Worksheet: /assets/worksheets/module10/module10-activity.md
Module 10 · Nanoscale

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Module 10 · Nanoscale

Pre-class preparation (10 min async) Read the graph representations content library entry Install NetworkX: `pip install networkx` Minute-by-minute plan 00:00-08:00 | Graph abstraction choices Show the same circuit as: (a) 3D EM rendering, (b) adjacency matrix, (c) node-link diagram. "These are three views of the same biology. Today we work with (b) and (c)." Discussion: "What did we gain and lose in each transformation?" 08:00-20:00 | Graph build demo Live coding: load a synapse table, construct a NetworkX DiGraph, apply threshold, print basic stats. Visualize the graph with spring layout. Color nodes by cell type. "Notice: the spatial layout in this diagram is arbitrary. The graph doesn't know where neurons are in the brain." 20:00-34:00 | Metric computation Hands-on: learners compute degree distribution, clustering coefficient, and average path length. Plot degree distribution (log-log). Is it heavy-tailed? Compute clustering and compare to a random graph (NetworkX: `nx.watts_strogatz_graph` for comparison). 34:00-46:00 | Interpretation and null concerns "Your clustering coefficient is 3× higher than the random graph. What does that mean biologically?" Discuss: spatial proximity as a confound. Would a spatially constrained null model change the conclusion? Walk through one example: reciprocal connections. Count in real data vs degree-preserving null. 46:00-60:00 | Competency check Each learner writes a 1-paragraph graph analysis summary: Schema (nodes, edges, threshold) Two metrics with values and null-model comparisons One biological interpretation and one limitation Exit ticket: "Name one reason a graph metric might be misleading in your dataset."