Opinion Dynamics on Directed Complex Networks

Replication and variation study for Fraiman, Lin, and Olvera-Cravioto (2024), arXiv:2209.00969v2.

The project implements the paper's linear stochastic opinion recursion on directed graphs, reproduces Figures 1-7, and adds topology, selective-exposure, bot, and community-structure variations.

Report

The current paper draft is maintained locally as report.tex. The TeX source and PDF files are treated as local submission/build artifacts and are intentionally ignored by git, including any locally compiled report.pdf or reference PDFs kept outside version control.

To rebuild the PDF while keeping LaTeX auxiliary files out of the repository root:

mkdir -p build/latex
pdflatex -interaction=nonstopmode -halt-on-error -output-directory=build/latex report.tex
pdflatex -interaction=nonstopmode -halt-on-error -output-directory=build/latex report.tex
cp build/latex/report.pdf report.pdf

Setup

python3 -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt

Core Replications

python3 scripts/replicate_fig1_to_3.py
python3 scripts/replicate_fig4.py
python3 scripts/replicate_fig5.py
python3 scripts/replicate_fig6.py
python3 scripts/replicate_fig7.py
python3 scripts/validate_theorem1.py

Variation Studies

python3 scripts/variation1_topology.py
python3 scripts/variation2_beta_scan.py
python3 scripts/variation3_bot_scan.py
python3 scripts/variation4_community.py

Generated figures are saved in figures/.

Notes

• The original paper does not report random seeds, iteration counts, or ensemble replicates, so these scripts use documented seeds and iteration limits.
• Figure 4 reports a 10-seed standard-error check. Variations 1 and 4 report 5-seed mean ± standard error summaries; the remaining baseline figures and variation scans are single-run unless otherwise noted.
• Figures 1-3 use a coupled-chain convergence diagnostic to check decay of the initial-condition effect.
• Variation 1 should be interpreted as topology/degree-distribution sensitivity; mean degree and low-degree mass are reported because they can confound a pure heavy-tail comparison.
• Variation 4 should be interpreted as a finite-network community-alignment check, not a full modularity sweep.