Hypergraph_RD

Python package for Random and Dynamical Hypergraph Computation

Library Requirement

• mandatory: random, itertools, numpy
• optional: networkx, hypernetx, xgi

Structure

• HyperRD.Hgraph: store all class objects
  • Hgraph.Create: undirected hypergraph object, including the following features and methods:
    • Features:
      • vertices: python set of vertices
      • vertices_dict: python dictionary of vertices
      • vertices_weight: python list of vertex weights (still developed)
      • edges: python set of hyperedges
      • edges_dict: python dictionary of hyperedges
      • edges_weight: python list of hyperedge weights (still developed)
      • inci_matrix: numpy matrix of an incidence matrix representation
    • Methods:
      • add_vertex(): add a vertex
      • add_edge(): add a hyperedge
      • dict_of_vertices(): return vertices in terms of an encoded dictionary
      • dict_of_edges(): return hyperedges in terms of an encoded dictionary
      • degree_vertex(): return a degree of a vertex
      • degree_edge(): return a degree of a hyperedge
      • diag_vertex(): return a numpy diagonal matrix of vertex degrees
      • diag_edge(): return a numpy diagonal matrix of hyperedge degrees
      • remove_vertex(): remove a vertex
      • remove_edge(): remove a hyperedge
      • incidence_matrix(): calculate an incidence matrix and store this matrix in inci_matrix
      • copy(): make a copy of graph
  • Hgraph.Create_Normal: undirected normal graph object, including the following features and methods:
    • Features:
      • vertices: number of vertices
      • adj: adjacency list of graph
    • Methods:
      • add_edge(): add edge
      • dfs_utility(): depth-first search algorithm to traverse the graph
      • connected_components(): return a list of connected components
      • copy(): make a copy of graph
  • Hgraph.Create_Direct: directed hypergraph object (inherit class of Create), including the following features and methods:
    • Features:
      • edges_direct: set of directed hyperedges, in form [start, end], where start and end are subsets of vertex set
    • Methods:
      • add_edge_direct(): add a directed hyperedge
  • Hgraph.Multilayer: multilayer hypergraph object, including the following features and methods:
    • Features:
      • layers: list of hypergraphs
      • interlink: set of interlinking hyperedge
    • Methods:
      • add_graph(): add layer
      • add_interlink(): add interlinking hyperedge
      • number_of_layer: return number of layers

Analyze tools

• HyperRD.Halgorithm: tools to analyze hypergraphs
  • vertex_connected(): check if two vertices are connected
  • graph_connected(): check if a hypergraph is fully connected
  • components_connected(): return a list of connected components in the hypergraph
  • simple_reduction(): reduce hypergraph to simple hypergraph (has no repeated hyperedge)
  • graph_expansion(): expand a hypergraph to a normal graph, based on chapter 2 of this book Hypergraph Computation
    • mode == 'clique': clique expansion
    • mode == 'star': star expansion or birpartite equivalence
    • mode == 'line': line expansion (still developed)
• HyperRD.Hmetric: metrics on hypergraphs
  • density(): return the density of hypergraph
  • girth(): return the size of the smallest non-empty hyperedge in the hypergraph
  • average_vertex_degree(): return the average degree across all vertices in the hypergraph
  • average_edge_size(): return the average size across all edges in the hypergraph

Random hypergraph generator

• HyperRD.Hrandom: generate random hypergraphs
  • simple_matrix(): each element of an incidence matrix will be set value 1 randomly with probability p (uniform distribution)
  • simple_bipartite(): create a random hypergraph with probability p (uniform distribution)
  • simple_powersets(): create a random hypergraph with probability p, based on the random choice of all possible edges (power set of vertices) (uniform distribution)
  • simple_order(): similar to simple_powersets(), but the degree of each hyperedge has a bound (the cardinality of the hyperedge is less than a fixed integer) (uniform distribution)
  • k_uniform(): create a k-uniform hypergraph with probability p (uniform distribution)

Stochastic processes on hypergraph

• HyperRD.Hdynamic: analyze stochastic processes on hypergraph
  • transit_prob_matrix(): return a uniform transition probability matrix of hypergraph (simple random walk)

Switch to other platforms

• HyperRD.Htranslate: change to other platforms (check the optional section of library requirement)
  • hyperrd_to_networkx(): switch from Hgraph.Create_Normal object to NetworkX object
  • hyperrd_to_hypernetx(): switch from Hgraph.Create object to HyperNetX object
  • hyperrd_to_xgi(): switch from Hgraph.Create object to XGI object