"""Base class for undirected hypergraphs."""
import random
from collections import defaultdict
from collections.abc import Hashable, Iterable
from copy import copy, deepcopy
from itertools import count
from warnings import warn
from ..exception import IDNotFound, XGIError, frozen
from ..utils import IDDict, update_uid_counter
from .views import EdgeView, NodeView
__all__ = ["Hypergraph"]
[docs]class Hypergraph:
r"""A hypergraph is a collection of subsets of a set of *nodes* or *vertices*.
A hypergraph is a pair :math:`(V, E)`, where :math:`V` is a set of elements called
*nodes* or *vertices*, and :math:`E` is a set whose elements are subsets of
:math:`V`, that is, each :math:`e \in E` satisfies :math:`e \subset V`. The
elements of :math:`E` are called *hyperedges* or simply *edges*.
The Hypergraph class allows any hashable object as a node and can associate
attributes to each node, edge, or the hypergraph itself, in the form of key/value
pairs. In this representation, multiedges are allowed.
Parameters
----------
incoming_data : input hypergraph data, optional
Data to initialize the hypergraph. If None (default), an empty
hypergraph is created, i.e. one with no nodes or edges.
The data can be in the following formats:
* hyperedge list
* hyperedge dictionary
* 2-column Pandas dataframe (bipartite edges)
* Incidence matrix: numpy ndarray or scipy.sparse array
* Hypergraph object
* SimplicialComplex object
**attr : dict, optional
Attributes to add to the hypergraph as key, value pairs.
By default, None.
See Also
--------
~xgi.core.simplicialcomplex.SimplicialComplex
~xgi.core.dihypergraph.DiHypergraph
Notes
-----
Unique IDs are assigned to each node and edge internally and are used to refer to
them throughout.
The `attr` keyword arguments are added as hypergraph attributes. To add node or edge
attributes see :meth:`add_node` and :meth:`add_edge`.
In addition to the methods listed in this page, other methods defined in the `stats`
package are also accessible via the `Hypergraph` class. For more details, see the
`tutorial
<https://xgi.readthedocs.io/en/stable/api/tutorials/focus_6.html>`_.
Examples
--------
>>> import xgi
>>> H = xgi.Hypergraph([[1, 2, 3], [4], [5, 6], [6, 7, 8]])
>>> H.nodes
NodeView((1, 2, 3, 4, 5, 6, 7, 8))
>>> H.edges
EdgeView((0, 1, 2, 3))
"""
_node_dict_factory = IDDict
_node_attr_dict_factory = IDDict
_edge_dict_factory = IDDict
_edge_attr_dict_factory = IDDict
_net_attr_dict_factory = dict
def __getstate__(self):
"""Function that allows pickling.
Returns
-------
dict
The keys label the hyeprgraph dict and the values
are dictionarys from the Hypergraph class.
Notes
-----
This allows the python multiprocessing module to be used.
"""
return {
"_edge_uid": self._edge_uid,
"_net_attr": self._net_attr,
"_node": self._node,
"_node_attr": self._node_attr,
"_edge": self._edge,
"_edge_attr": self._edge_attr,
}
def __setstate__(self, state):
"""Function that allows unpickling of a hypergraph.
Parameters
----------
state
The keys access the dictionary names the values are the
dictionarys themselves from the Hypergraph class.
Notes
-----
This allows the python multiprocessing module to be used.
"""
self._edge_uid = state["_edge_uid"]
self._net_attr = state["_net_attr"]
self._node = state["_node"]
self._node_attr = state["_node_attr"]
self._edge = state["_edge"]
self._edge_attr = state["_edge_attr"]
self._nodeview = NodeView(self)
self._edgeview = EdgeView(self)
def __init__(self, incoming_data=None, **attr):
self._edge_uid = count()
self._net_attr = self._net_attr_dict_factory()
self._node = self._node_dict_factory()
self._node_attr = self._node_attr_dict_factory()
self._edge = self._edge_dict_factory()
self._edge_attr = self._edge_attr_dict_factory()
self._nodeview = NodeView(self)
"""A :class:`~xgi.core.views.NodeView` of the hypergraph."""
self._edgeview = EdgeView(self)
"""An :class:`~xgi.core.views.EdgeView` of the hypergraph."""
if incoming_data is not None:
# This import needs to happen when this function is called, not when it is
# defined. Otherwise, a circular import error would happen.
from ..convert import to_hypergraph
to_hypergraph(incoming_data, create_using=self)
self._net_attr.update(attr) # must be after convert
def __str__(self):
"""Returns a short summary of the hypergraph.
Returns
-------
string
Hypergraph information
"""
try:
return (
f"{type(self).__name__} named {self['name']} "
f"with {self.num_nodes} nodes and {self.num_edges} hyperedges"
)
except XGIError:
return (
f"Unnamed {type(self).__name__} with "
f"{self.num_nodes} nodes and {self.num_edges} hyperedges"
)
def __iter__(self):
"""Iterate over the nodes.
Returns
-------
iterator
An iterator over all nodes in the hypergraph.
"""
return iter(self._node)
def __contains__(self, n):
"""Check for if a node is in this hypergraph.
Parameters
----------
n : hashable
node ID
Returns
-------
bool
Whether the node exists in the hypergraph.
"""
try:
return n in self._node
except TypeError:
return False
def __len__(self):
"""Number of nodes in the hypergraph.
Returns
-------
int
The number of nodes in the hypergraph.
See Also
--------
num_nodes : identical method
num_edges : number of edges in the hypergraph
"""
return len(self._node)
def __getitem__(self, attr):
"""Read hypergraph attribute."""
try:
return self._net_attr[attr]
except KeyError:
raise XGIError("This attribute has not been set.")
def __setitem__(self, attr, val):
"""Write hypergraph attribute."""
self._net_attr[attr] = val
def __getattr__(self, attr):
stat = getattr(self.nodes, attr, None)
word = "nodes"
if stat is None:
stat = getattr(self.edges, attr, None)
word = "edges"
if stat is None:
word = None
raise AttributeError(
f"{attr} is not a method of Hypergraph or a "
"recognized NodeStat or EdgeStat"
)
def func(node=None, *args, **kwargs):
val = stat(*args, **kwargs).asdict()
return val if node is None else val[node]
func.__doc__ = f"""Equivalent to H.{word}.{attr}.asdict(). For accepted *args and
**kwargs, see documentation of H.{word}.{attr}."""
return func
def __lshift__(self, H2):
"""Adds the edges of a hypergraph to the current hypergraph
and updates the attributes.
The node/edge attributes of the new hypergraph take precedence.
Relabels all the edge IDs to preserve all the edges but
keeps the node labels the same.
Parameters
----------
H2 : Hypergraph
The hypergraph to update with.
Returns
-------
Hypergraph
The updated hypergraph
Notes
-----
Addition is not quite commutative; the attributes of nodes and edges
may be overwritten depending on whether they are first or second
to be added. In addition, the edge IDs are assigned based on the order
in which the edges are added, but does not functionally change the
structure of the hypergraph.
Examples
--------
>>> import xgi
>>> H1 = xgi.Hypergraph([[1, 2], [2, 3]])
>>> H2 = xgi.Hypergraph([[1, 3, 4]])
>>> H = H1 << H2
>>> H.edges.members()
[{1, 2}, {2, 3}, {1, 3, 4}]
"""
tempH = Hypergraph()
tempH.add_nodes_from(zip(self._node.keys(), self._node_attr.values()))
tempH.add_nodes_from(zip(H2._node.keys(), H2._node_attr.values()))
tempH.add_edges_from(zip(self._edge.values(), self._edge_attr.values()))
tempH.add_edges_from(zip(H2._edge.values(), H2._edge_attr.values()))
tempH._net_attr = deepcopy(self._net_attr)
tempH._net_attr.update(deepcopy(H2._net_attr))
return tempH
@property
def nodes(self):
"""A :class:`NodeView` of this network."""
return self._nodeview
@property
def edges(self):
"""An :class:`EdgeView` of this network."""
return self._edgeview
@property
def num_nodes(self):
"""The number of nodes in the hypergraph.
Returns
-------
int
The number of nodes in the hypergraph.
See Also
--------
num_edges : returns the number of edges in the hypergraph
Examples
--------
>>> import xgi
>>> hyperedge_list = [[1, 2], [2, 3, 4]]
>>> H = xgi.Hypergraph(hyperedge_list)
>>> H.num_nodes
4
"""
return len(self._node)
@property
def num_edges(self):
"""The number of edges in the hypergraph.
Returns
-------
int
The number of edges in the hypergraph.
See Also
--------
num_nodes : returns the number of nodes in the hypergraph
Examples
--------
>>> import xgi
>>> hyperedge_list = [[1, 2], [2, 3, 4]]
>>> H = xgi.Hypergraph(hyperedge_list)
>>> H.num_edges
2
"""
return len(self._edge)
[docs] def add_node(self, node, **attr):
"""Add one node with optional attributes.
Parameters
----------
node : node
A node can be any hashable Python object except None.
attr : keyword arguments, optional
Set or change node attributes using key=value.
See Also
--------
add_nodes_from
set_node_attributes
Notes
-----
If node is already in the hypergraph, its attributes are still updated.
"""
if node not in self._node:
self._node[node] = set()
self._node_attr[node] = self._node_attr_dict_factory()
self._node_attr[node].update(attr)
[docs] def add_nodes_from(self, nodes_for_adding, **attr):
"""Add multiple nodes with optional attributes.
Parameters
----------
nodes_for_adding : iterable
An iterable of nodes (list, dict, set, etc.).
OR
An iterable of (node, attribute dict) tuples.
Node attributes are updated using the attribute dict.
attr : keyword arguments, optional (default= no attributes)
Update attributes for all nodes in nodes.
Node attributes specified in nodes as a tuple take
precedence over attributes specified via keyword arguments.
See Also
--------
add_node
set_node_attributes
"""
for n in nodes_for_adding:
try:
newnode = n not in self._node
newdict = attr
except TypeError:
n, ndict = n
newnode = n not in self._node
newdict = attr.copy()
newdict.update(ndict)
if newnode:
self._node[n] = set()
self._node_attr[n] = self._node_attr_dict_factory()
self._node_attr[n].update(newdict)
[docs] def remove_node(self, n, strong=False, remove_empty=True):
"""Remove a single node.
The removal may be weak (default) or strong. In weak removal, the node is
removed from each of its containing edges. If it is contained in any singleton
edges, then these are also removed. In strong removal, all edges containing the
node are removed, regardless of size.
Parameters
----------
n : node
A node in the hypergraph
strong : bool, optional
Whether to execute weak or strong removal. By default, False.
remove_empty : bool, optional
Whether to remove empty edges. By default, True.
Raises
------
XGIError
If n is not in the hypergraph.
See Also
--------
remove_nodes_from
"""
edge_neighbors = self._node[n]
del self._node[n]
del self._node_attr[n]
if strong:
for e in edge_neighbors:
node_neighbors = self._edge[e]
del self._edge[e]
del self._edge_attr[e]
for node in node_neighbors.difference({n}):
self._node[node].remove(e)
else: # weak removal
for edge in edge_neighbors:
self._edge[edge].remove(n)
if not self._edge[edge] and remove_empty:
del self._edge[edge]
del self._edge_attr[edge]
[docs] def remove_nodes_from(self, nodes, strong=False, remove_empty=True):
"""Remove multiple nodes.
Parameters
----------
nodes : iterable
An iterable of nodes.
strong : bool, optional
Whether to execute weak or strong removal. By default, False.
remove_empty : bool, optional
Whether to remove empty edges. By default, True.
See Also
--------
remove_node
"""
for n in nodes:
if n not in self:
warn(f"Node {n} not in hypergraph")
continue
self.remove_node(n, strong=strong, remove_empty=remove_empty)
[docs] def set_node_attributes(self, values, name=None):
"""Sets node attributes from a given value or dictionary of values.
Parameters
----------
values : scalar value, dict-like
What the node attribute should be set to. If `values` is
not a dictionary, then it is treated as a single attribute value
that is then applied to every node in `H`. This means that if
you provide a mutable object, like a list, updates to that object
will be reflected in the node attribute for every node.
The attribute name will be `name`.
If `values` is a dict or a dict of dict, it should be keyed
by node to either an attribute value or a dict of attribute key/value
pairs used to update the node's attributes.
name : string, optional
Name of the node attribute to set if values is a scalar, by default None.
See Also
--------
set_edge_attributes
add_node
add_nodes_from
Notes
-----
After computing some property of the nodes of a hypergraph, you may
want to assign a node attribute to store the value of that property
for each node.
If you provide a list as the second argument, updates to the list
will be reflected in the node attribute for each node.
If you provide a dictionary of dictionaries as the second argument,
the outer dictionary is assumed to be keyed by node to an inner
dictionary of node attributes for that node.
Note that if the dictionary contains nodes that are not in `G`, the
values are silently ignored.
"""
# Set node attributes based on type of `values`
if name is not None: # `values` must not be a dict of dict
if isinstance(values, dict): # `values` is a dict
for n, v in values.items():
try:
self._node_attr[n][name] = v
except IDNotFound:
warn(f"Node {n} does not exist!")
else: # `values` is a constant
for n in self:
self._node_attr[n][name] = values
else: # `values` must be dict of dict
try:
for n, d in values.items():
try:
self._node_attr[n].update(d)
except IDNotFound:
warn(f"Node {n} does not exist!")
except (TypeError, ValueError, AttributeError):
raise XGIError("Must pass a dictionary of dictionaries")
[docs] def add_edge(self, members, idx=None, **attr):
"""Add one edge with optional attributes.
Parameters
----------
members : Iterable
An iterable of the ids of the nodes contained in the new edge.
idx : hashable, optional
Id of the new edge. If None (default), a unique numeric ID will be created.
**attr : dict, optional
Attributes of the new edge.
Raises
-----
XGIError
If `members` is empty.
See Also
--------
add_edges_from : Add a collection of edges.
set_edge_attributes
Examples
--------
Add edges with or without specifying an edge id.
>>> import xgi
>>> H = xgi.Hypergraph()
>>> H.add_edge([1, 2, 3])
>>> H.add_edge([3, 4], idx='myedge')
>>> H.edges
EdgeView((0, 'myedge'))
Access attributes using square brackets. By default no attributes are created.
>>> H.edges[0]
{}
>>> H.add_edge([1, 4], color='red', place='peru')
>>> H.edges
EdgeView((0, 'myedge', 1))
>>> H.edges[1]
{'color': 'red', 'place': 'peru'}
"""
members = set(members)
if idx in self._edge.keys(): # check that uid is not present yet
warn(f"uid {idx} already exists, cannot add edge {members}")
return
uid = next(self._edge_uid) if idx is None else idx
self._edge[uid] = set()
for node in members:
if node not in self._node:
self._node[node] = set()
self._node_attr[node] = self._node_attr_dict_factory()
self._node[node].add(uid)
self._edge[uid].add(node)
self._edge_attr[uid] = self._edge_attr_dict_factory()
self._edge_attr[uid].update(attr)
if idx: # set self._edge_uid correctly
update_uid_counter(self, idx)
[docs] def add_edges_from(self, ebunch_to_add, **attr):
r"""Add multiple edges with optional attributes.
Parameters
----------
ebunch_to_add : Iterable
An iterable of edges. This may be an iterable of iterables (Format 1),
where each element contains the members of the edge specified as valid node
IDs. Alternatively, each element could also be a tuple in any of the
following formats:
* Format 2: 2-tuple (members, edge_id), or
* Format 3: 2-tuple (members, attr), or
* Format 4: 3-tuple (members, edge_id, attr),
where `members` is an iterable of node IDs, `edge_id` is a hashable to use
as edge ID, and `attr` is a dict of attributes. Finally, `ebunch_to_add` may
be a dict of the form `{edge_id: edge_members}` (Format 5).
Formats 2 and 3 are unambiguous because `attr` dicts are not hashable, while
`id`s must be. In Formats 2-4, each element of `ebunch_to_add` must have
the same length, i.e. you cannot mix different formats. The iterables
containing edge members cannot be strings.
**attr : kwargs, optional
Additional attributes to be assigned to all edges. Attribues specified via
`ebunch_to_add` take precedence over `attr`.
See Also
--------
add_edge : Add a single edge.
add_weighted_edges_from : Convenient way to add weighted edges.
set_edge_attributes
Notes
-----
Adding the same edge twice will create a multi-edge. Currently
cannot add empty edges; the method skips over them.
Examples
--------
>>> import xgi
>>> H = xgi.Hypergraph()
When specifying edges by their members only, numeric edge IDs will be assigned
automatically.
>>> H.add_edges_from([[0, 1], [1, 2], [2, 3, 4]])
>>> H.edges.members(dtype=dict)
{0: {0, 1}, 1: {1, 2}, 2: {2, 3, 4}}
Custom edge ids can be specified using a dict.
>>> H = xgi.Hypergraph()
>>> H.add_edges_from({'one': [0, 1], 'two': [1, 2], 'three': [2, 3, 4]})
>>> H.edges.members(dtype=dict)
{'one': {0, 1}, 'two': {1, 2}, 'three': {2, 3, 4}}
You can use the dict format to easily add edges from another hypergraph.
>>> H2 = xgi.Hypergraph()
>>> H2.add_edges_from(H.edges.members(dtype=dict))
>>> H.edges == H2.edges
True
Alternatively, edge ids can be specified using an iterable of 2-tuples.
>>> H = xgi.Hypergraph()
>>> H.add_edges_from([([0, 1], 'one'), ([1, 2], 'two'), ([2, 3, 4], 'three')])
>>> H.edges.members(dtype=dict)
{'one': {0, 1}, 'two': {1, 2}, 'three': {2, 3, 4}}
Attributes for each edge may be specified using a 2-tuple for each edge.
Numeric IDs will be assigned automatically.
>>> H = xgi.Hypergraph()
>>> edges = [
... ([0, 1], {'color': 'red'}),
... ([1, 2], {'age': 30}),
... ([2, 3, 4], {'color': 'blue', 'age': 40}),
... ]
>>> H.add_edges_from(edges)
>>> {e: H.edges[e] for e in H.edges}
{0: {'color': 'red'}, 1: {'age': 30}, 2: {'color': 'blue', 'age': 40}}
Attributes and custom IDs may be specified using a 3-tuple for each edge.
>>> H = xgi.Hypergraph()
>>> edges = [
... ([0, 1], 'one', {'color': 'red'}),
... ([1, 2], 'two', {'age': 30}),
... ([2, 3, 4], 'three', {'color': 'blue', 'age': 40}),
... ]
>>> H.add_edges_from(edges)
>>> {e: H.edges[e] for e in H.edges}
{'one': {'color': 'red'}, 'two': {'age': 30}, 'three': {'color': 'blue', 'age': 40}}
"""
# format 5 is the easiest one
if isinstance(ebunch_to_add, dict):
for idx, members in ebunch_to_add.items():
if idx in self._edge.keys(): # check that uid is not present yet
warn(f"uid {idx} already exists, cannot add edge {members}.")
continue
try:
self._edge[idx] = set(members)
except TypeError as e:
raise XGIError("Invalid ebunch format") from e
for n in members:
if n not in self._node:
self._node[n] = set()
self._node_attr[n] = self._node_attr_dict_factory()
self._node[n].add(idx)
self._edge_attr[idx] = self._edge_attr_dict_factory()
update_uid_counter(self, idx)
return
# in formats 1-4 we only know that ebunch_to_add is an iterable, so we iterate
# over it and use the firs element to determine which format we are working with
new_edges = iter(ebunch_to_add)
try:
first_edge = next(new_edges)
except StopIteration:
return
try:
first_elem = list(first_edge)[0]
except TypeError:
first_elem = None
format1, format2, format3, format4 = False, False, False, False
if isinstance(first_elem, Iterable):
if all(isinstance(e, str) for e in first_edge):
format1 = True
elif len(first_edge) == 2 and issubclass(type(first_edge[1]), Hashable):
format2 = True
elif len(first_edge) == 2:
format3 = True
elif len(first_edge) == 3:
format4 = True
else:
format1 = True
if (format1 and isinstance(first_edge, str)) or (
not format1 and isinstance(first_elem, str)
):
raise XGIError("Members cannot be specified as a string")
# now we may iterate over the rest
e = first_edge
while True:
if format1:
members, idx, eattr = e, next(self._edge_uid), {}
elif format2:
members, idx, eattr = e[0], e[1], {}
elif format3:
members, idx, eattr = e[0], next(self._edge_uid), e[1]
elif format4:
members, idx, eattr = e[0], e[1], e[2]
if idx in self._edge.keys(): # check that uid is not present yet
warn(f"uid {idx} already exists, cannot add edge {members}.")
else:
try:
self._edge[idx] = set(members)
except TypeError as e:
raise XGIError("Invalid ebunch format") from e
for n in members:
if n not in self._node:
self._node[n] = set()
self._node_attr[n] = self._node_attr_dict_factory()
self._node[n].add(idx)
self._edge_attr[idx] = self._edge_attr_dict_factory()
self._edge_attr[idx].update(attr)
self._edge_attr[idx].update(eattr)
try:
e = next(new_edges)
except StopIteration:
if format2 or format4:
update_uid_counter(self, idx)
break
[docs] def add_weighted_edges_from(self, ebunch, weight="weight", **attr):
"""Add multiple weighted edges with optional attributes.
Parameters
----------
ebunch_to_add : iterable of edges
Each edge given in the list or container will be added
to the graph. The edges must be given as tuples of
the form (node1, node2, ..., noden, weight).
weight : string, optional
The attribute name for the edge weights to be added,
by default "weight".
attr : keyword arguments, optional
Edge attributes to add/update for all edges.
See Also
--------
add_edge : Add a single edge.
add_edges_from : Add multiple edges.
set_edge_attributes
get_edge_attributes
Notes
-----
Adding the same edge twice creates a multiedge.
Examples
--------
>>> import xgi
>>> H = xgi.Hypergraph()
>>> edges = [(0, 1, 0.3), (0, 2, 0.8)]
>>> H.add_weighted_edges_from(edges)
>>> H.edges[0]
{'weight': 0.3}
"""
try:
self.add_edges_from(
((edge[:-1], {weight: edge[-1]}) for edge in ebunch), **attr
)
except KeyError:
XGIError("Empty or invalid edges specified.")
[docs] def set_edge_attributes(self, values, name=None):
"""Set the edge attributes from a value or a dictionary of values.
Parameters
----------
values : scalar value, dict-like
What the edge attribute should be set to. If `values` is
not a dictionary, then it is treated as a single attribute value
that is then applied to every edge in `H`. This means that if
you provide a mutable object, like a list, updates to that object
will be reflected in the edge attribute for each edge. The attribute
name will be `name`.
If `values` is a dict or a dict of dict, it should be keyed
by edge ID to either an attribute value or a dict of attribute
key/value pairs used to update the edge's attributes.
name : string, optional
Name of the edge attribute to set if values is a scalar. By default, None.
See Also
--------
set_node_attributes
add_edge
add_edges_from
Notes
-----
Note that if the dict contains edge IDs that are not in `H`, they are
silently ignored.
"""
if name is not None:
# `values` does not contain attribute names
try:
for e, value in values.items():
try:
self._edge_attr[e][name] = value
except IDNotFound:
warn(f"Edge {e} does not exist!")
except AttributeError:
# treat `values` as a constant
for e in self._edge:
self._edge_attr[e][name] = values
else:
try:
for e, d in values.items():
try:
self._edge_attr[e].update(d)
except IDNotFound:
warn(f"Edge {e} does not exist!")
except AttributeError:
raise XGIError(
"name property has not been set and a "
"dict-of-dicts has not been provided."
)
[docs] def double_edge_swap(self, n_id1, n_id2, e_id1, e_id2):
"""Swap the edge memberships of two selected nodes, given two edges.
Parameters
----------
n_id1 : hashable
The ID of the first node, originally a member of the first edge.
n_id2 : hashable
The ID of the second node, originally a member of the second edge.
e_id1 : hashable
The ID of the first edge.
e_id2 : hashable
The ID of the second edge.
Raises
------
IDNotFound
If user specifies nodes or edges that do not exist or
nodes that are not part of edges.
XGIError
If the swap does not preserve edge sizes.
Examples
--------
>>> import xgi
>>> H = xgi.Hypergraph([[1, 2, 3], [3, 4]])
>>> H.double_edge_swap(1, 4, 0, 1)
>>> H.edges.members()
[{2, 3, 4}, {1, 3}]
"""
# Assign edges to modify
try:
# Initialize temporary copies to modify
temp_memberships1 = self._node[n_id1].copy()
temp_memberships2 = self._node[n_id2].copy()
temp_members1 = self._edge[e_id1].copy()
temp_members2 = self._edge[e_id2].copy()
# remove old nodes from edges
temp_members1.remove(n_id1)
temp_members2.remove(n_id2)
# swap nodes
temp_members1.add(n_id2)
temp_members2.add(n_id1)
# Now we handle the memberships
# remove old nodes from edges
temp_memberships1.remove(e_id1)
temp_memberships2.remove(e_id2)
# swap nodes
temp_memberships1.add(e_id2)
temp_memberships2.add(e_id1)
except KeyError as e:
raise IDNotFound(
"One of the nodes specified doesn't belong to the specified edge."
) from e
if (
len(temp_memberships1) != len(self._node[n_id1])
or len(temp_memberships2) != len(self._node[n_id2])
or len(temp_members1) != len(self._edge[e_id1])
or len(temp_members2) != len(self._edge[e_id2])
):
raise XGIError("This swap does not preserve edge sizes.")
self._node[n_id1] = temp_memberships1
self._node[n_id2] = temp_memberships2
self._edge[e_id1] = temp_members1
self._edge[e_id2] = temp_members2
[docs] def random_edge_shuffle(self, e_id1=None, e_id2=None):
"""Randomly redistributes nodes between two hyperedges.
The process is as follows:
1. randomly select two hyperedges
2. place all their nodes into a single bucket
3. randomly redistribute the nodes between those two hyperedges
Parameters
----------
e_id1 : node ID, optional
ID of first edge to shuffle.
e_id2 : node ID, optional
ID of second edge to shuffle.
Note
----
After shuffling, the sizes of the two hyperedges are unchanged.
Edge IDs and attributes are also unchanged.
If the same node appears in both hyperedges, then this is still true after reshuffling.
If either `e_id1` or `e_id2` is not provided, then two random edges are selected.
References
----------
Philip S Chodrow, 2020.
"Configuration models of random hypergraphs."
Journal of Complex Networks, 8(3).
https://doi.org/10.1093/comnet/cnaa018
Example
-------
>>> import xgi
>>> random.seed(42)
>>> H = xgi.Hypergraph([[1, 2, 3], [3, 4], [4, 5]])
>>> H.random_edge_shuffle()
>>> H.edges.members()
[{2, 4, 5}, {3, 4}, {1, 3}]
"""
if len(self._edge) < 2:
raise ValueError("Hypergraph must have at least two edges.")
# select two random edges
if e_id1 is None or e_id2 is None:
e_id1, e_id2 = random.sample(list(self._edge), 2)
# extract edges (lists of nodes)
e1 = self._edge[e_id1]
e2 = self._edge[e_id2]
# nodes in both edges should not be shuffled
nodes_both = e1 & e2
e1 -= nodes_both
e2 -= nodes_both
# put all nodes in a single bucket
nodes = e1 | e2
# randomly redistribute nodes between the two edges
e1_new = set(random.sample(list(nodes), len(e1)))
e2_new = nodes - e1_new
# update edge memberships
for n_id in e1_new & e2:
self._node[n_id].remove(e_id2)
self._node[n_id].add(e_id1)
for n_id in e2_new & e1:
self._node[n_id].remove(e_id1)
self._node[n_id].add(e_id2)
# add nodes in both edges back
e1_new |= nodes_both
e2_new |= nodes_both
# update hypergraph
self._edge[e_id1] = e1_new
self._edge[e_id2] = e2_new
[docs] def add_node_to_edge(self, edge, node):
"""Add one node to an existing edge.
If the node or edge IDs do not exist, they are created.
Parameters
----------
edge : hashable
edge ID
node : hashable
node ID
See Also
--------
add_node
add_edge
remove_node_from_edge
Examples
--------
>>> import xgi
>>> H = xgi.Hypergraph()
>>> H.add_edge(['apple', 'banana'], 'fruits')
>>> H.add_node_to_edge('fruits', 'pear')
>>> H.add_node_to_edge('veggies', 'lettuce')
>>> d = H.edges.members(dtype=dict)
>>> {i: sorted(list(e)) for i, e in d.items()}
{'fruits': ['apple', 'banana', 'pear'], 'veggies': ['lettuce']}
"""
if edge not in self._edge:
self._edge[edge] = set()
self._edge_attr[edge] = {}
if node not in self._node:
self._node[node] = set()
self._node_attr[node] = {}
self._edge[edge].add(node)
self._node[node].add(edge)
[docs] def remove_edge(self, idx):
"""Remove one edge.
Parameters
----------
idx : Hashable
edge ID to remove
Raises
------
XGIError
If no edge has that ID.
See Also
--------
remove_edges_from : Remove multiple edges.
"""
for node in self._edge[idx].copy():
self._node[node].remove(idx)
del self._edge[idx]
del self._edge_attr[idx]
[docs] def remove_edges_from(self, ebunch):
"""Remove multiple edges.
Parameters
----------
ebunch: Iterable
Edges to remove.
Raises
------
xgi.exception.IDNotFound
If an id in ebunch is not part of the network.
See Also
--------
remove_edge : remove a single edge.
"""
for idx in ebunch:
for node in self._edge[idx].copy():
self._node[node].remove(idx)
del self._edge[idx]
del self._edge_attr[idx]
[docs] def remove_node_from_edge(self, edge, node, remove_empty=True):
"""Remove a node from an existing edge.
Parameters
----------
edge : hashable
The edge ID
node : hashable
The node ID
remove_empty : bool, optional
Whether empty edges are removed. By default, True.
Raises
------
XGIError
If either the node or edge does not exist.
See Also
--------
remove_node
remove_edge
add_node_to_edge
Notes
-----
If edge is left empty as a result of removing node from it, the edge is also
removed.
"""
if edge not in self._edge:
raise XGIError(f"Edge {edge} not in the hypergraph")
elif node not in self._node:
raise XGIError(f"Node {node} not in the hypergraph")
elif node not in self._edge[edge]:
raise XGIError(f"Edge {edge} does not contain node {node}")
else:
self._edge[edge].remove(node)
self._node[node].remove(edge)
if not self._edge[edge] and remove_empty:
del self._edge[edge]
del self._edge_attr[edge]
[docs] def update(self, *, edges=None, nodes=None):
"""Add nodes or edges to the hypergraph.
Parameters
----------
edges : Iterable, optional
Edges to be added. By default, None.
nodes : Iterable, optional
Nodes to be added. By default, None.
See Also
--------
add_edges_from: Add multiple edges.
add_nodes_from: Add multiple nodes.
"""
if nodes:
self.add_nodes_from(nodes)
if edges:
self.add_edges_from(edges)
[docs] def clear(self, remove_net_attr=True):
"""Remove all nodes and edges from the graph.
Also removes node and edge attributes, and optionally hypergraph attributes.
Parameters
----------
remove_net_attr : bool, optional
Whether to remove hypergraph attributes as well.
By default, True.
"""
self._node.clear()
self._node_attr.clear()
self._edge.clear()
self._edge_attr.clear()
if remove_net_attr:
self._net_attr.clear()
[docs] def clear_edges(self):
"""Remove all edges from the graph without altering any nodes."""
for node in self.nodes:
self._node[node] = set()
self._edge.clear()
self._edge_attr.clear()
[docs] def merge_duplicate_edges(
self, rename="first", merge_rule="first", multiplicity=None
):
"""Merges edges which have the same members.
Parameters
----------
rename : str, optional
Either "first" (default), "tuple", or "new".
If "first", the new edge ID is the first of the sorted
duplicate edge IDs. If "tuple", the new edge ID is a
tuple of the sorted duplicate edge IDs. If "new", a
new ID will be selected automatically.
merge_rule : str, optional
Either "first" (default) or "union".
If "first", takes the attributes of the first duplicate.
If "union", takes the set of attributes of all the duplicates.
multiplicity : str, optional
The attribute in which to store the multiplicity of the hyperedge,
by default None.
Raises
------
XGIError
If invalid rename or merge_rule specified.
Warns
-----
If the user chooses merge_rule="union". Tells the
user that they can no longer draw based on this stat.
Examples
--------
>>> import xgi
>>> edges = [{1, 2}, {1, 2}, {1, 2}, {3, 4, 5}, {3, 4, 5}]
>>> edge_attrs = dict()
>>> edge_attrs[0] = {"color": "blue"}
>>> edge_attrs[1] = {"color": "red", "weight": 2}
>>> edge_attrs[2] = {"color": "yellow"}
>>> edge_attrs[3] = {"color": "purple"}
>>> edge_attrs[4] = {"color": "purple", "name": "test"}
>>> H = xgi.Hypergraph(edges)
>>> H.set_edge_attributes(edge_attrs)
>>> H.edges
EdgeView((0, 1, 2, 3, 4))
There are several ways to rename the duplicate edges after merging:
1. The merged edge ID is the first duplicate edge ID.
>>> H1 = H.copy()
>>> H1.merge_duplicate_edges()
>>> H1.edges
EdgeView((0, 3))
2. The merged edge ID is a tuple of all the duplicate edge IDs.
>>> H2 = H.copy()
>>> H2.merge_duplicate_edges(rename="tuple")
>>> H2.edges
EdgeView(((0, 1, 2), (3, 4)))
3. The merged edge ID is assigned a new edge ID.
>>> H3 = H.copy()
>>> H3.merge_duplicate_edges(rename="new")
>>> H3.edges
EdgeView((5, 6))
We can also specify how we would like to combine the attributes
of the merged edges:
1. The attributes are the attributes of the first merged edge.
>>> H4 = H.copy()
>>> H4.merge_duplicate_edges()
>>> H4.edges[0]
{'color': 'blue'}
2. The attributes are the union of every attribute that each merged
edge has. If a duplicate edge doesn't have that attribute, it is set
to None.
>>> H5 = H.copy()
>>> H5.merge_duplicate_edges(merge_rule="union")
>>> H5.edges[0] == {'color': {'blue', 'red', 'yellow'}, 'weight':{2, None}}
True
3. We can also set the attributes to the intersection, i.e.,
if a particular attribute is the same across the duplicate
edges, we use this attribute, otherwise, we set it to None.
>>> H6 = H.copy()
>>> H6.merge_duplicate_edges(merge_rule="intersection")
>>> H6.edges[0] == {'color': None, 'weight': None}
True
>>> H6.edges[3] == {'color': 'purple', 'name': None}
True
We can also choose to store the multiplicity of the edge
as an attribute. The user simply provides the string of
the attribute which stores it. Note that this will not prevent
other attributes from being over written (e.g., weight), so
be careful that the attribute is not already in use.
>>> H7 = H.copy()
>>> H7.merge_duplicate_edges(multiplicity="mult")
>>> H7.edges[0]['mult'] == 3
True
"""
dups = []
hashes = defaultdict(list)
for idx, members in self._edge.items():
hashes[frozenset(members)].append(idx)
new_edges = list()
for members, dup_ids in hashes.items():
if len(dup_ids) > 1:
dups.extend(dup_ids)
if rename == "first":
new_id = sorted(dup_ids)[0]
elif rename == "tuple":
new_id = tuple(sorted(dup_ids))
elif rename == "new":
new_id = next(self._edge_uid)
else:
raise XGIError("Invalid ID renaming scheme!")
if merge_rule == "first":
idx = min(dup_ids)
new_attrs = deepcopy(self._edge_attr[idx])
elif merge_rule == "union":
attrs = {field for idx in dup_ids for field in self._edge_attr[idx]}
new_attrs = {
attr: {self._edge_attr[idx].get(attr) for idx in dup_ids}
for attr in attrs
}
elif merge_rule == "intersection":
attrs = {field for idx in dup_ids for field in self._edge_attr[idx]}
set_attrs = {
attr: {self._edge_attr[idx].get(attr) for idx in dup_ids}
for attr in attrs
}
new_attrs = {
attr: (None if len(val) != 1 else next(iter(val)))
for attr, val in set_attrs.items()
}
else:
raise XGIError("Invalid merge rule!")
if multiplicity is not None:
new_attrs[multiplicity] = len(dup_ids)
new_edges.append((members, new_id, new_attrs))
self.remove_edges_from(dups)
self.add_edges_from(new_edges)
if merge_rule == "union":
warn(
"You will not be able to color/draw by "
"merged attributes with xgi.draw()!"
)
[docs] def copy(self):
"""A deep copy of the hypergraph.
A deep copy of the hypergraph, including node, edge, and hypergraph attributes.
Returns
-------
H : Hypergraph
A copy of the hypergraph.
"""
cp = self.__class__()
nn = self.nodes
cp.add_nodes_from((n, deepcopy(attr)) for n, attr in nn.items())
ee = self.edges
cp.add_edges_from(
(e, idx, deepcopy(self.edges[idx]))
for idx, e in ee.members(dtype=dict).items()
)
cp._net_attr = deepcopy(self._net_attr)
cp._edge_uid = copy(self._edge_uid)
return cp
[docs] def dual(self):
"""The dual of the hypergraph.
In the dual, nodes become edges and edges become nodes.
Returns
-------
Hypergraph
The dual of the hypergraph.
"""
dual = self.__class__()
nn = self.nodes
dual.add_edges_from(
(nn.memberships(n), n, deepcopy(attr)) for n, attr in nn.items()
)
ee = self.edges
dual.add_nodes_from((e, deepcopy(attr)) for e, attr in ee.items())
dual._net_attr = deepcopy(self._net_attr)
return dual
[docs] def cleanup(
self,
isolates=False,
singletons=False,
multiedges=False,
connected=True,
relabel=True,
in_place=True,
):
"""Removes potentially undesirable artifacts from the hypergraph.
Parameters
----------
isolates : bool, optional
Whether isolated nodes are allowed, by default False.
singletons : bool, optional
Whether singleton edges are allowed, by default False.
multiedges : bool, optional
Whether multiedges are allowed, by default False.
connected : bool, optional
Whether the returned hypergraph should be connected. If true,
returns the hypergraph induced on the largest connected component.
By default, False.
relabel : bool, optional
Whether to convert all node and edge labels to sequential integers, by
default True.
in_place : bool, optional
Whether to modify the current hypergraph or output a new one, by default
True.
"""
if in_place:
_H = self
else:
_H = self.copy()
if not multiedges:
_H.merge_duplicate_edges()
if not singletons:
_H.remove_edges_from(_H.edges.singletons())
if not isolates:
_H.remove_nodes_from(_H.nodes.isolates())
if connected:
from ..algorithms import largest_connected_hypergraph
largest_connected_hypergraph(_H, in_place=True)
if relabel:
from ..utils import convert_labels_to_integers
convert_labels_to_integers(_H, in_place=True)
return _H
[docs] def freeze(self):
"""Method for freezing a hypergraph which prevents it from being modified
See Also
--------
~xgi.exception.frozen : Method that raises an error when a user tries to modify the hypergraph
is_frozen : Check whether a hypergraph is frozen
Examples
--------
>>> import xgi
>>> edges = [[1, 2], [2, 3, 4]]
>>> H = xgi.Hypergraph(edges)
>>> H.freeze()
>>> H.add_node(5)
Traceback (most recent call last):
xgi.exception.XGIError: Frozen higher-order network can't be modified
"""
self.add_node = frozen
self.add_nodes_from = frozen
self.remove_node = frozen
self.remove_nodes_from = frozen
self.add_edge = frozen
self.add_edges_from = frozen
self.add_weighted_edges_from = frozen
self.remove_edge = frozen
self.remove_edges_from = frozen
self.add_node_to_edge = frozen
self.remove_node_from_edge = frozen
self.clear = frozen
self.frozen = True
@property
def is_frozen(self):
"""Checks whether a dihypergraph is frozen
Returns
-------
bool
True if hypergraph is frozen, false if not.
See Also
--------
freeze : A method to prevent a hypergraph from being modified.
Examples
--------
>>> import xgi
>>> edges = [[1, 2], [2, 3, 4]]
>>> H = xgi.Hypergraph(edges)
>>> H.freeze()
>>> H.is_frozen
True
"""
try:
return self.frozen
except AttributeError:
return False
