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Rendering formule matematiche docstring
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hiper/metrics/average_hyperedge_cardinality.py

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@@ -21,9 +21,9 @@ class AverageHyperedgeCardinality:
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The Average Hyperedge Cardinality measures the mean size of hyperedges
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in the hypergraph after perturbation:
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AHC = (1/|E'|) * Σ|e| for e ∈ E'
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``AHC = (1/|E'|) * Σ|e|`` for ``e ∈ E'``
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where E' is the set of hyperedges after perturbation and |e| is the
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where E' is the set of hyperedges after perturbation and ``|e|`` is the
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cardinality (size) of hyperedge e.
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This metric provides insight into how perturbations affect the

hiper/metrics/hyperedge_fragmentation.py

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@@ -21,13 +21,13 @@ class HyperedgeFragmentationIndex:
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The Hyperedge Fragmentation Index measures how much the original hyperedges
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have been fragmented by a perturbation:
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HFI = 1 - (1/|E|) * Σ(|e ∩ V'|/|e|) for e ∈ E
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``HFI = 1 - (1/|E|) * Σ(|e ∩ V'|/|e|)`` for ``e ∈ E``
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where:
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- E is the original set of hyperedges
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- V' is the set of nodes after perturbation
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- e ∩ V' is the intersection of original hyperedge e with remaining nodes
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- |e| is the original size of hyperedge e
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- ``e ∩ V'`` is the intersection of original hyperedge e with remaining nodes
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- ``|e|`` is the original size of hyperedge e
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A value of 0.0 indicates no fragmentation (all hyperedges intact),
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while 1.0 indicates complete fragmentation (all hyperedges destroyed).

hiper/metrics/hyperedge_integrity.py

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@@ -20,7 +20,7 @@ class HyperedgeIntegrity:
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The Hyperedge Integrity measures the fraction of hyperedges that remain
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in the hypergraph after a perturbation:
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HI = |E'| / |E|
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``HI = |E'| / |E|``
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where E is the original set of hyperedges and E' is the set of hyperedges
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after perturbation.

hiper/metrics/redundancy.py

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@@ -18,8 +18,8 @@ class RedundancyCoefficient:
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The redundancy coefficient measures the average degree of normalized
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overlap between pairs of hyperedges in the hypergraph.
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Formula: ρ(H) = (1/|E|²) * Σ(|e1 ∩ e2| / √(|e1| * |e2|))
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for all pairs e1, e2 ∈ E with e1 ≠ e2.
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Formula: ``ρ(H) = (1/|E|²) * Σ(|e1 ∩ e2| / √(|e1| * |e2|))``
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for all pairs ``e1, e2 ∈ E`` with ``e1 ≠ e2``.
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"""
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@staticmethod

hiper/metrics/swalk.py

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@@ -18,8 +18,8 @@ class SwalkEfficiency:
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The s-walk efficiency measures how efficiently nodes can reach each
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other via s-walks, computed as the average of inverse distances.
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Formula: ℰs(H) = (1/(|V|(|V|-1))) * Σ(1/d_H^s(u,v))
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for all pairs u,v ∈ V with u ≠ v.
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Formula: ``ℰs(H) = (1/(|V|(|V|-1))) * Σ(1/d_H^s(u,v))``
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for all pairs ``u,v ∈ V`` with ``u ≠ v``.
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"""
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def __init__(self, s: int = 1):

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