wehub-resource-sync
71 lines
2.2 KiB
Python
71 lines
2.2 KiB
Python
from easygraph.exception import EasyGraphError
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__all__ = [
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"hypergraph_density",
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]
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def hypergraph_density(hg, ignore_singletons=False):
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r"""Hypergraph density.
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The density of a hypergraph is the number of existing edges divided by the number of
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possible edges.
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Let `H` have :math:`n` nodes and :math:`m` hyperedges. Then,
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* `density(H) =` :math:`\frac{m}{2^n - 1}`,
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* `density(H, ignore_singletons=True) =` :math:`\frac{m}{2^n - 1 - n}`.
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Here, :math:`2^n` is the total possible number of hyperedges on `H`, from which we
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subtract :math:`1` because the empty hyperedge is not considered. We subtract an
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additional :math:`n` when singletons are not considered.
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Now assume `H` has :math:`a` edges with order :math:`1` and :math:`b` edges with
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order :math:`2`. Then,
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* `density(H, order=1) =` :math:`\frac{a}{{n \choose 2}}`,
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* `density(H, order=2) =` :math:`\frac{b}{{n \choose 3}}`,
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* `density(H, max_order=1) =` :math:`\frac{a}{{n \choose 1} + {n \choose 2}}`,
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* `density(H, max_order=1, ignore_singletons=True) =` :math:`\frac{a}{{n \choose 2}}`,
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* `density(H, max_order=2) =` :math:`\frac{m}{{n \choose 1} + {n \choose 2} + {n \choose 3}}`,
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* `density(H, max_order=2, ignore_singletons=True) =` :math:`\frac{m}{{n \choose 2} + {n \choose 3}}`,
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Parameters
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---------
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order : int, optional
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If not None, only count edges of the specified order.
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By default, None.
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max_order : int, optional
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If not None, only count edges of order up to this value, inclusive.
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By default, None.
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ignore_singletons : bool, optional
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Whether to consider singleton edges. Ignored if `order` is not None and
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different from :math:`0`. By default, False.
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See Also
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--------
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:func:`incidence_density`
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Notes
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-----
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If both `order` and `max_order` are not None, `max_order` is ignored.
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"""
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n = hg.num_v
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numer = len(hg.e[0])
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if n < 1:
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raise EasyGraphError("Density not defined for empty hypergraph")
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if numer < 1:
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return 0.0
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denom = 2**n - 1
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if ignore_singletons:
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denom -= n
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try:
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return numer / float(denom)
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except ZeroDivisionError:
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return 0.0
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