Hypergraph Properties

HAT implements computations for a series of standard graph and hypergraph theoretic properties. These properties are computed on either hypergraph or graph objects, which are created based on incidence and adjacency matrices respectively.

H = HAT.hypergraph.hypergraph(W)    # Create a hypergraph with an incidence matrix W
G = HAT.graph.graph(A)              # Create a graph with an adjacency matrix A

Diameter

The diameter is defined as the maximum minimum distance between any two vertices in a graph or hypergraph.

diameter = H.diameter

Clustering Coefficient

The clustering coefficient of a graph or hypergraph is the average clustering coefficient of all vertices. For any given vertex, the vertex clustering coefficient is calculated as

gamma = H.clusteringCoefficient     # Hypergraph clustering coeffficient
gammaI = H.clusteringCoefficient(i) # Clustering coefficient of vertex i

Average Distance

The average distance is the pairwise distance between any two vertices.

avgDistane = H.averageDistance
  1. Diameter

  2. Clustering Coefficient

  3. Average Distance

  4. etc.