dhgraph: Python Module for Directed Hypergraphs

Introduction

A directed hypergraph is a generalization of digraph. It consists of a set of vertices V and a set of hyperarcs H. A hyperarc is a pair of a nonempty subset of V (called head) and a vertex of V (called tail).

Definitions and terminology used in this document as well as source code are based on the paper: Giorgio Ausiello, Luigi Laura, Directed hypergraphs: Introduction and fundamental algorithms: A survey , Theoretical Computer Science, Volume 658, Part B, 2017, Pages 293-306.

Installation

$ pip install dhgraph

Usage

Let us import dhgraph module, create an empty directed hypergraph, and add hyperarcs.

from dhgraph import DirectedHypergraph

g = DirectedHypergraph()

#   1 ---> 2
#   |      |
#   v      v
#   4----> 3

h1 = g.add_hyperarc((1,),  2)
h2 = g.add_hyperarc((1,),  4)
h3 = g.add_hyperarc((4, 2), 3)
H = {h1, h2, h3} # Set of hyperarc identifiers, used later.

# NOTE: The order of vertices in head is not important.
assert h3 == g.add_hyperarc((2, 4), 3)

# NOTE: The output of get_head() is sorted.
assert g.get_head(h3) == (2,4)
assert g.get_tail(h3) == 3

As above, add_hyperarc() has a tuple of vertex identifiers, head, as its 1st argument and a vertex identifier, tail, as its 2nd argument, and returns the identifier of a hyperarc having the head and the tail.

The vertices and the hyperarcs added so far can be obtained by get_vertices() and get_hyperarcs(), which respecitvely return a tuple of vertex identifiers and a tuple of hyperarc identifiers.

assert set(g.get_vertices())  == {1, 2, 3, 4}
assert set(g.get_hyperarcs()) == H

Hyperarcs that are incident to a vertex can be obtained by get_hyperarcs_from() and get_hyperarcs_to(), which respectively return a tuple of hyperarcs emanating from a vertex and a tuple of hyperarcs pointing to a vertex.

assert set(g.get_hyperarcs_from(1)) == {h1, h2}
assert set(g.get_hyperarcs_to(3))   == {h3}
# exceptional cases
assert set(g.get_hyperarcs_from(3)) == set()
assert set(g.get_hyperarcs_to(1))   == set()

Vertices and hyperarcs can be assigned labels, if necessary, when they are added.

gg = DirectedHypergraph()

gg.add_vertex(1, label="A")
gg.add_vertex(2, label="B")
gg.add_vertex(3, label="C")
gg.add_vertex(4, label="D")
h1 = gg.add_hyperarc((1,),   2, label="A->B")
h2 = gg.add_hyperarc((1,),   4, label="A->D")
h3 = gg.add_hyperarc((4, 2), 3, label="B,D->C")

assert gg.get_vertex_label(4)    == "D"
assert gg.get_hyperarc_label(h3) == "B,D->C"

If you prefer to use vertex labels, call add_vertex() for all vertices to which labels are to be assigned and then call add_hyperarc(). Otherwise, add_hyperarc() will add vertices appearing in head or tail so that they have vertex identifiers as their labels.

A directed hypergraph can be rendered as follows.

gg.render(filename="sample", format="png")

As a result, sample.png will be generated. The arguments of render() are the same as those of render() of Graphviz. See User Guide of Graphviz .

Bugs/Requests/Discussions

Please report bugs and requests from GitHub Issues , and ask questions from GitHub Discussions .

License

Please see LICENSE .