Directed Edge Weight Encoding

---
name: directed-edge-weight-encoding
description: 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.
license: CC-BY-4.0
metadata:
  edam_operation: http://edamontology.org/operation_3680
  edam_topics:
  - http://edamontology.org/topic_0602
  - http://edamontology.org/topic_3172
  - http://edamontology.org/topic_0092
  tools:
  - R
  - MInfer
  - igraph
  - tidygraph
  license_tier: open
  provenance_tier: literature
derived_from:
- doi: 10.1016/j.cmpb.2025.108672
  title: MInfer
evidence_spans:
- MInfer is an R package
- MInfer is an R package designed for analyzing metabolomics data
claims: []
provenance:
  collection: https://w3id.org/holobiomicslab/asb-skill/collection/metabolomics/v2
  assembled_by: scripts/collect_metabolomics_collection.py
  sources:
  - build: coll_minfer_cq
    doi: 10.1016/j.cmpb.2025.108672
    title: MInfer
  dedup_kept_from: coll_minfer_cq
schema_version: 0.2.0
attribution:
  generator: AgenticScienceBuilder
  original_doi: 10.1016/j.cmpb.2025.108672
  all_source_dois:
  - 10.1016/j.cmpb.2025.108672
  zenodo_doi: 10.5281/zenodo.20794027
  curators: []
  promoter: Louis-Félix Nothias
  sponsor: CNRS & Université Côte d'Azur
---

# 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"