{
  "annotation_id": "d9a1a796-0366-4912-b949-18a4343d4b5b",
  "date_created": "2026-03-02T18:01:17.759000Z",
  "date_modified": "2026-03-02T18:01:17.759000Z",
  "file_hash": "07ade878edc926fc6f7092ea9883349d0585b5b1eef0d89325bb4a6fa2ba2ed8",
  "private": false,
  "record": {
    "abstract": "Modular structure is ubiquitous among complex networks. We note that most\nsuch systems are subject to multiple structural and functional constraints,\ne.g., minimizing the average path length and the total number of links, while\nmaximizing robustness against perturbations in node activity. We show that the\noptimal networks satisfying these three constraints are characterized by the\nexistence of multiple subnetworks (modules) sparsely connected to each other.\nIn addition, these modules have distinct hubs, resulting in an overall\nheterogeneous degree distribution.",
    "arxiv_id": "physics/0703033",
    "authors": [
      "Raj Kumar Pan",
      "Sitabhra Sinha"
    ],
    "categories": [
      "physics.soc-ph",
      "cond-mat.dis-nn"
    ],
    "doi": "10.1103/PhysRevE.76.045103",
    "journal_ref": "Phys. Rev. E 76, 045103(R) (2007) (4 pages)",
    "title": "Modular networks emerge from multiconstraint optimization",
    "url": "https://arxiv.org/abs/physics/0703033"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6167a563-7b72-4236-ad90-52f7348320ff",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}