{
  "handle": "DegreeEntropy",
  "ref": "DegreeEntropy#a793",
  "stub": "a793",
  "semaId": "sema:DegreeEntropy#mh:SHA-256:a793cb859ab1915416e67b257770a97d4810b2ac751247aba715530df2d69297",
  "layer": "Infrastructure",
  "category": "Primitives",
  "gloss": "Entropy of how connectivity is spread over the nodes of a network: local heterogeneity",
  "mechanism": "For a network with N nodes and degree sequence k_1..k_N, normalise each node's share of all links, p_i = k_i / sum_j k_j, and take H_d = -sum_i p_i log2 p_i, the {{shannon_entropy}} of that share. H_d is maximal (log2 N) when every node has the same degree and falls as connectivity concentrates on a few hubs. It measures how evenly interaction opportunities are distributed, i.e. the diversity of local pathways. For a directed graph, k_i can be the total degree (in-degree plus out-degree), which discards direction. Note that p_i runs over nodes, not over degree classes, so H_d also grows with N; normalise by N or by an area to compare networks of different size.",
  "invariants": [
    "Computed from the degree sequence alone, ignoring which nodes are linked to which",
    "Maximal when all degrees are equal, minimal when connectivity is concentrated",
    "Grows with node count, so raw values are not comparable across networks of different size"
  ],
  "failureModes": [
    "Comparing raw H_d across networks of different size and mistaking size for structure",
    "Using total degree on a directed graph and losing the asymmetry between incoming and outgoing links",
    "Confusing this node-share form with the entropy of the degree distribution P(k)"
  ],
  "ring": 1,
  "tier": 1,
  "aliases": {
    "shannon_entropy": "ShannonEntropy"
  },
  "buildsOn": [
    {
      "handle": "ShannonEntropy",
      "type": "references",
      "alias": "shannon_entropy",
      "url": "/knowledge-graph/ShannonEntropy/",
      "json": "/knowledge-graph/ShannonEntropy.json"
    }
  ],
  "usedBy": [
    {
      "handle": "SpectralEntropy",
      "type": "composes_with",
      "alias": "degree_entropy",
      "url": "/knowledge-graph/SpectralEntropy/",
      "json": "/knowledge-graph/SpectralEntropy.json"
    },
    {
      "handle": "InteractionSequenceEntropySignature",
      "type": "composes_with",
      "alias": "degree_entropy",
      "url": "/knowledge-graph/InteractionSequenceEntropySignature/",
      "json": "/knowledge-graph/InteractionSequenceEntropySignature.json"
    },
    {
      "handle": "SecondOrderInteractionNetwork",
      "type": "composes_with",
      "alias": "degree_entropy",
      "url": "/knowledge-graph/SecondOrderInteractionNetwork/",
      "json": "/knowledge-graph/SecondOrderInteractionNetwork.json"
    }
  ],
  "sources": {
    "research": [],
    "works": [
      {
        "kind": "thesis",
        "label": "Kevin Do, PhD thesis on ant collective behaviour (NCSU, 2026)",
        "note": "Ch. 1.3.3, Eqs. 1.6-1.7; Ch. 3.2.2, Eq. 3.26",
        "url": ""
      }
    ],
    "homePage": false
  },
  "url": "/knowledge-graph/DegreeEntropy/",
  "graphUrl": "/knowledge-graph#DegreeEntropy",
  "directory": "/knowledge-graph/patterns.json"
}