{
  "abstract": "We study the first-order effects of nodal inputs on edge flows of network systems through controllability Gramians. We consider both discrete- and continuous-time dynamics subject to impulse and step input disturbances. To characterize their impact on network behavior, we introduce the notion of a vulnerability matrix (VM) and provide explicit Gramian-based expressions that reveal the critical role played by the interplay between network topology and dynamics. For the class of directed line networks, we particularize these closed-form expressions in terms of edge weights, input duration, and graph distance to the nodal input. Numerical simulations on directed line and random Erdős-Rényi networks show a tight correspondence between influential nodes identified with the VM and conventional time-domain performance metrics, such as $\\mathscr{H}_2$ and $\\mathscr{H}_{\\infty}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06897",
  "author_total": 3,
  "authors": [
    {
      "name": "Prasad Vilas Chanekar"
    },
    {
      "name": "Bala Kameshwar Poolla"
    },
    {
      "name": "Jorge Cortés"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cg0ybjpp5dmmj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06897",
  "fulltext_url": null,
  "id": "cg0ybjpp5dmmj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06897",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "3109|Complex Network Analysis Techniques"
    ]
  ],
  "openalex": "W7212057341",
  "pdf_url": "https://arxiv.org/pdf/2609.06897",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cg0ybjpp5dmmj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06897",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06897"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Gramian-Informed Framework for Edge Flow Network Analysis Against Nodal Attacks",
  "title_text": "Gramian-Informed Framework for Edge Flow Network Analysis Against Nodal Attacks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/cg0ybjpp5dmmj",
  "venue": "arXiv",
  "versions": []
}