# Directed Edge Weight Encoding

> Use when after computing a Jacobian matrix from covariance data and extracting directed edges representing metabolite interactions, use this skill when you need to communicate the magnitude and direction of metabolite-to-metabolite influences in a single integrated visualization.

- Skill: `holobiomicslab/directed-edge-weight-encoding` (Agent Skill)
- Install (CLI): `npx skillmds@latest add holobiomicslab/directed-edge-weight-encoding`
- Raw SKILL.md: https://api.skillmd.com/api/skills/holobiomicslab/directed-edge-weight-encoding/raw
- Safety review: PASS (external: skill-scanner PASS, skillspector PASS)
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- License: CC-BY-4.0
- Author: HolobiomicsLab (https://skillmd.com/u/holobiomicslab)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/holobiomicslab/directed-edge-weight-encoding

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# directed-edge-weight-encoding

## Summary

Encode metabolite-to-metabolite interaction strengths and directionality as edge weights and visual properties (color, thickness, arrow direction) in network graphs derived from Jacobian matrices. This enables publication-quality visualization of dynamic metabolomic network topology where edge magnitude and sign reflect the quantitative influence of one metabolite on another.

## When to use

After computing a Jacobian matrix from covariance data and extracting directed edges representing metabolite interactions, use this skill when you need to communicate the magnitude and direction of metabolite-to-metabolite influences in a single integrated visualization. Specifically, when Jacobian coefficients vary substantially across the network (e.g., ranging from −2.5 to +1.8) and distinguishing strong vs. weak interactions visually is essential for biological interpretation.

## When NOT to use

- Jacobian matrix contains only zero coefficients or all interactions are below significance threshold — no meaningful edges to visualize.
- Input is already a pre-rendered network image or adjacency list without original coefficient values — weight encoding cannot be applied retroactively.
- Analysis goal is hypothesis-free network topology only (e.g., community detection, clustering) without need to communicate interaction magnitude or direction.

## Inputs

- Jacobian matrix (numerical matrix, rows/columns correspond to metabolites)
- Metabolite identifiers (KEGG IDs or chemical names corresponding to matrix dimensions)
- Network layout algorithm specification (optional; defaults to force-directed)

## Outputs

- Network graph object (igraph or tidygraph R object)
- Publication-quality network visualization (rendered figure with labeled nodes, weighted/colored directed edges)
- Edge list or weight table (data frame mapping metabolite pairs to interaction strength and direction)

## How to apply

Extract non-zero or statistically significant Jacobian coefficients as directed edges between metabolite nodes. Map edge weight magnitude to visual properties: assign line thickness or opacity proportional to the absolute value of the Jacobian coefficient, and use color (e.g., red for positive/activating, blue for negative/inhibitory interactions) to encode interaction direction. Apply a network layout algorithm (e.g., force-directed or hierarchical) to position nodes for clarity, then render the graph with labeled metabolites, weighted/colored edges, and a legend explaining the encoding scheme. Validate that the resulting visualization preserves the sign and rank order of coefficients from the original matrix.

## Related tools

- **MInfer** (R package providing Jacobian matrix computation and network visualization functions; includes visualize_heatmap() and visualize_3d() for rendering weighted network structures.) — https://github.com/cellbiomaths/MInfer
- **igraph** (R graph library for constructing network objects and applying layout algorithms to position nodes in 2D space.)
- **tidygraph** (R graph manipulation library for managing network nodes and edges with associated metadata (weights, directions, interaction types).)
- **R** (Runtime environment for loading Jacobian matrices, extracting edges, constructing graph objects, and rendering visualizations.)

## Examples

```
visualize_heatmap(jacobian_6C$J, title = "Jacobian Matrix - 6C")
```

## Evaluation signals

- Edge weights (line thickness, color intensity, or numeric labels) monotonically correspond to absolute Jacobian coefficient magnitudes — verify by spot-checking 3–5 edges against the original matrix values.
- Edge direction (arrow orientation or color polarity) accurately reflects the sign of each Jacobian coefficient: positive coefficients are visually distinct from negative ones.
- Network layout preserves relative spatial relationships: strongly connected metabolites are positioned close together, and isolated nodes are peripheral.
- Legend or figure caption unambiguously explains the encoding scheme (e.g., 'Red = activating interaction; Blue = inhibitory; Line thickness ∝ |coefficient|').
- Visualization is publication-ready: fonts are readable, node labels do not overlap excessively, and edge crossings are minimized by layout algorithm.

## Limitations

- Visualization quality degrades for large networks (>50 nodes) due to node/edge overlap; consider filtering to subnetworks of interest or using hierarchical or circular layouts.
- Color-based encoding of interaction direction may not be accessible to colorblind readers — use shape, texture, or supplementary numeric labels to encode direction redundantly.
- Jacobian matrix coefficients may reflect correlation structure rather than causal metabolite interactions; edge weights should not be interpreted as mechanistic reaction rates without additional biological validation.
- No changelog or version history available for MInfer, limiting reproducibility across future updates.

## Evidence

- [other] Extract edge information from the Jacobian matrix by identifying non-zero or significant coefficients that represent metabolite-to-metabolite interactions.: "Extract edge information from the Jacobian matrix by identifying non-zero or significant coefficients that represent metabolite-to-metabolite interactions."
- [other] Render the network visualization with metabolite labels, edge weights or colors to encode interaction strength and direction, and save as a publication-quality figure.: "Render the network visualization with metabolite labels, edge weights or colors to encode interaction strength and direction, and save as a publication-quality figure."
- [other] Construct a network graph object representing metabolites as nodes and Jacobian coefficients as directed edges using an R graph library (e.g., igraph or tidygraph).: "Construct a network graph object representing metabolites as nodes and Jacobian coefficients as directed edges using an R graph library (e.g., igraph or tidygraph)."
- [intro] MInfer provides tools for data preparation, covariance matrix generation, Jacobian matrix computation, and visualization of metabolite interaction networks: "MInfer provides tools for data preparation, covariance matrix generation, Jacobian matrix computation, and visualization of metabolite interaction networks"
- [readme] Visualize the Jacobian matrices using a heatmap or 3D plot: "Visualize the Jacobian matrices using a heatmap or 3D plot"