Analytics Engine

HyperMesh DB includes a built-in hypergraph analytics engine with 25 measures, computed in-process using SciPy sparse matrices.

Accessing analytics

Python

analytics = db.analytics("CoProximity")

# Structural
print(analytics.density())
print(analytics.uniformity())

# Centrality
pr = analytics.pagerank()      # dict: node_id → score
bc = analytics.betweenness()

# Spectral
sg = analytics.spectral_gap()
ac = analytics.algebraic_connectivity()

# Temporal
tb = analytics.temporal_burstiness()
ta = analytics.temporal_activity()

REST

curl -H "X-API-Key: hmdb_yourkey" \
  http://localhost:8000/v1/analytics/CoProximity/pagerank

TypeScript

const pr = await db.analytics("CoProximity", "pagerank");
console.log(pr.result);  // { "1": 0.23, "2": 0.31, ... }

All 25 measures

Structural

Measure	Description
`density`	Fraction of all possible hyperedges that are present
`uniformity`	Proportion of hyperedges with the modal edge size
`overlapping_coefficient`	Mean node participation across hyperedges
`redundancy`	Fraction of node pairs that share multiple hyperedges
`isolated_nodes`	Count of nodes in no hyperedge
`isolated_edges`	Count of hyperedges with no shared nodes

Degree / size distributions

Measure	Description
`node_degree`	Dict: node → number of hyperedges it belongs to
`edge_size`	Dict: edge_id → number of members

Centrality

Measure	Description
`betweenness`	Hyperedge betweenness centrality
`closeness`	Closeness centrality via star-expansion
`pagerank`	PageRank over the bipartite hyperedge graph
`harmonic_centrality`	Harmonic mean of inverse distances
`clique_number`	Size of the largest clique in the 2-section graph

Spectral

Measure	Description
`spectral_gap`	λ₂ − λ₁ of the normalised hypergraph Laplacian
`algebraic_connectivity`	Second-smallest Laplacian eigenvalue (Fiedler value)

Clustering

Measure	Description
`zhou_clustering`	Zhou et al. 2006 hypergraph clustering coefficient
`pairwise_clustering`	Fraction of co-member pairs that share another hyperedge
`modularity`	Louvain-style hypergraph modularity

s-walk (HNX-compatible)

Measure	Description
`s_adjacency`	s-adjacency matrix (edges sharing ≥ s nodes)
`s_distance`	Shortest s-walk distance between all hyperedge pairs
`s_connected_components`	Number of s-connected components
`s_diameter`	Diameter of the largest s-component

Temporal

Measure	Description
`temporal_activity`	Dict: node → number of distinct time buckets active
`temporal_burstiness`	Coefficient of variation of inter-event times per node
`temporal_coreness`	k-core decomposition of the temporal projection