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Network Science operators

5 operators in the network_science category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
NET_BETWEENNESSBetweenness centrality quantifying how often a node lies on shortest paths between all other node pairs.g(v) = \sum_{s \neq v \neq t} \frac{\sigma_{st}(v)}{\sigma_{st}}
NET_CLUSTERINGLocal clustering coefficient measuring the proportion of triangles among a node's neighbors in an undirected graph.C_i = \frac{2 |\{e_{jk}\}|}{k_i(k_i - 1)}, \quad j,k \in \mathcal{N}_i
NET_MODULARITYNewman-Girvan modularity measuring the quality of a community partition in a network.Q = \frac{1}{2m} \sum_{ij} \left(A_{ij} - \frac{k_i k_j}{2m}\right) \delta(c_i, c_j)
NET_PAGERANKPageRank centrality computing the stationary distribution of a random walk with damping on a directed graph.PR(i) = \frac{1-d}{N} + d \sum_{j \in B_i} \frac{PR(j)}{L(j)}
NET_SCALE_FREEPower-law degree distribution characteristic of scale-free networks with preferential attachment.P(k) \sim k^{-\gamma}, \quad 2 < \gamma < 3

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["NET_BETWEENNESS"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​