Module 10: Network Science and Graph Representation

Teaching Deck

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

Session Outcomes

• Learners can complete the module capability target.
• Learners can produce one evidence-backed artifact.
• Learners can state one limitation or uncertainty.

Agenda (60 min)

• 0-10 min: Frame and model
• 10-35 min: Guided practice
• 35-50 min: Debrief and misconception correction
• 50-60 min: Competency check + exit ticket

Capability Target

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

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).

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

60-Minute Run-of-Show

• Read the graph representations content library entry
• Install NetworkX: pip install networkx
• 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."

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.

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?"

Activity Output Checklist

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

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

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

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.

Exit Ticket

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

References (Instructor)

• Use module references listed on the module page.

Teaching Materials

• Module page: /modules/module10/
• Slide page: /modules/slides/module10/
• Worksheet: /assets/worksheets/module10/module10-activity.md