Module higher_order 

Higher-order network analysis.

Implements:

• Motif tensors – third-order adjacency tensors capturing 3-node motifs.
• Topological features – Betti numbers from a simplicial complex bridge.
• Cellular sheaves – basic sheaf theory on graphs (restriction maps, coboundary operator, Hodge Laplacian).

References

• Benson et al., “Three hypergraph eigenvector centralities”, SIAM J. Math. Data Sci. 2019.
• Hansen & Ghrist, “Toward a spectral theory of cellular sheaves”, J. Applied and Computational Topology, 2019.
• Battiston et al., “Networks beyond pairwise interactions”, Physics Reports 2020.

Structs

CellularSheaf

A cellular sheaf on an undirected graph.

MotifTensor

A third-order motif tensor T[i,j,k] encoding 3-node interaction patterns.

TopologicalFeatures

Topological feature vector derived from a SimplicialComplex.

Functions

directed_motif_tensor

Build a directed motif tensor that distinguishes different 3-node motif types (feed-forward, cycle, etc.) in a directed graph.

trivial_sheaf_from_graph

Build a trivial sheaf from an existing graph (uses usize-indexed nodes).