{"id":50500709,"url":"https://github.com/prof-faustus/m840","last_synced_at":"2026-06-02T11:02:28.674Z","repository":{"id":360568971,"uuid":"1250753240","full_name":"prof-faustus/M840","owner":"prof-faustus","description":"Spectral stability analysis of weighted complete graph Laplacians under structured perturbations, focusing on algebraic connectivity, Rayleigh quotient bounds, cut-capacity bottlenecks, vertex augmentation, Schur complements, and reproducible Python figures.","archived":false,"fork":false,"pushed_at":"2026-05-27T00:08:54.000Z","size":966,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":0,"default_branch":"main","last_synced_at":"2026-05-27T02:12:08.063Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"TeX","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/prof-faustus.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":"CITATION.cff","codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2026-05-27T00:02:37.000Z","updated_at":"2026-05-27T00:08:58.000Z","dependencies_parsed_at":null,"dependency_job_id":null,"html_url":"https://github.com/prof-faustus/M840","commit_stats":null,"previous_names":["prof-faustus/m840"],"tags_count":null,"template":false,"template_full_name":null,"purl":"pkg:github/prof-faustus/M840","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/prof-faustus%2FM840","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/prof-faustus%2FM840/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/prof-faustus%2FM840/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/prof-faustus%2FM840/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/prof-faustus","download_url":"https://codeload.github.com/prof-faustus/M840/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/prof-faustus%2FM840/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":33818568,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-05-26T15:22:16.424Z","status":"online","status_checked_at":"2026-06-02T02:00:07.132Z","response_time":109,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2026-06-02T11:02:27.603Z","updated_at":"2026-06-02T11:02:28.663Z","avatar_url":"https://github.com/prof-faustus.png","language":"TeX","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Spectral Stability of Weighted Complete Graph Laplacians under Structured Perturbations\n\nThis repository contains the LaTeX source, bibliography, reproducibility code, generated figures, and compiled PDF for the M840 dissertation:\n\n**Spectral Stability of Weighted Complete Graph Laplacians under Structured Perturbations**\n\nStudent number: J0840966  \nDate: May 2026\n\n## Repository contents\n\n```text\nmain.tex                 LaTeX dissertation source\nreferences.bib           BibTeX bibliography database\nmain.bbl                 Compiled bibliography file used for reproducible builds\nmain.pdf                 Compiled dissertation PDF\nrequirements.txt         Python dependencies for regenerating figures and tables\ncode/make_figures.py     Full Python script for numerical figures and table output\nfigures/                 Generated PDF figures used in Chapter 7\ntwo_block_table.tex      Generated numerical table used in Chapter 7\nCITATION.cff             Citation metadata for this repository\nUPLOAD_CHECKLIST.md      Practical upload and verification checklist\n```\n\n## Mathematical focus\n\nThe dissertation is a proof-led algebraic graph theory study of weighted complete graph Laplacians. It focuses on:\n\n- algebraic connectivity;\n- Rayleigh quotient methods;\n- cut-capacity certificates;\n- two-block weighted complete graph spectra;\n- vertex augmentation;\n- Schur complements;\n- interlacing and perturbation estimates;\n- numerical illustrations of structured versus diffuse perturbations.\n\nThe main conclusion is that complete support alone does not guarantee spectral robustness: algebraic connectivity is governed by the geometry of the edge weights, especially cross-cut capacity.\n\n## Reproducing the numerical material\n\nCreate a Python environment and install the dependencies:\n\n```bash\npython -m venv .venv\nsource .venv/bin/activate\npip install -r requirements.txt\n```\n\nRegenerate the figures and table:\n\n```bash\npython code/make_figures.py\n```\n\nThis recreates the files in `figures/` and regenerates the numerical table used in Chapter 7.\n\n## Compiling the dissertation\n\nThe repository includes `main.bbl`, so the document can be compiled even in environments without BibTeX:\n\n```bash\npdflatex main.tex\npdflatex main.tex\n```\n\nFor a full BibTeX rebuild:\n\n```bash\npdflatex main.tex\nbibtex main\npdflatex main.tex\npdflatex main.tex\n```\n\n## Reproducibility note\n\nThe numerical examples are illustrative checks of the analytic formulae and inequalities. They are not used as substitutes for the proofs. Randomness appears only in the diffuse perturbation comparison, where the script fixes the random seed for reproducibility.\n\n## AI-use statement\n\nAI was used for searching, LaTeX organisation, checking formatting, and reproducibility packaging.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fprof-faustus%2Fm840","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fprof-faustus%2Fm840","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fprof-faustus%2Fm840/lists"}