xgi.stats.edgestats

Edge statistics.

This module is part of the stats package, and it defines edge-level statistics. That is, each function defined in this module is assumed to define an edge-quantity mapping. Each callable defined here is accessible via a Network object, or a EdgeView object. For more details, see the tutorial.

Examples

>>> import xgi
>>> H = xgi.Hypergraph([[1, 2, 3], [2, 3, 4, 5], [3, 4, 5]])
>>> H.order()
{0: 2, 1: 3, 2: 2}
>>> H.edges.order.asdict()
{0: 2, 1: 3, 2: 2}

Functions

xgi.stats.edgestats.attrs(net, bunch, attr=None, missing=None)[source]

Access edge attributes.

Parameters:

net (xgi.Hypergraph) – The network.
bunch (Iterable) – Nodes in net.
attr (str | None (default)) – If None, return all attributes. Otherwise, return a single attribute with name attr.
missing (Any) – Value to impute in case an edge does not have an attribute with name attr. Default is None.

Returns:

If attr is None, return a nested dict of the form {edge: {“attr”: val}}. Otherwise, return a simple dict of the form {edge: val}.

Return type:

dict

Notes

When requesting all attributes (i.e. when attr is None), no value is imputed.

Examples

>>> import xgi
>>> H = xgi.Hypergraph()
>>> edges = [
...     ([0, 1], 'one', {'color': 'red'}),
...     ([1, 2], 'two', {'color': 'black', 'age': 30}),
...     ([2, 3, 4], 'three', {'color': 'blue', 'age': 40}),
... ]
>>> H.add_edges_from(edges)

Access all attributes as different types.

>>> H.edges.attrs.asdict() 
{'one': {'color': 'red'},
 'two': {'color': 'black', 'age': 30},
 'three': {'color': 'blue', 'age': 40}}
>>> H.edges.attrs.asnumpy() 
array([{'color': 'red'},
       {'color': 'black', 'age': 30},
       {'color': 'blue', 'age': 40}],
       dtype=object)

Access a single attribute as different types.

>>> H.edges.attrs('color').asdict()
{'one': 'red', 'two': 'black', 'three': 'blue'}
>>> H.edges.attrs('color').aslist()
['red', 'black', 'blue']

By default, None is imputed when a node does not have the requested attribute.

>>> H.edges.attrs('age').asdict()
{'one': None, 'two': 30, 'three': 40}

Use missing to change the imputed value.

>>> H.edges.attrs('age', missing=100).asdict()
{'one': 100, 'two': 30, 'three': 40}

xgi.stats.edgestats.order(net, bunch, degree=None)[source]

Edge order.

The order of an edge is the number of nodes it contains minus 1.

Parameters:

net (xgi.Hypergraph) – The network.
bunch (Iterable) – Edges in net.
degree (int | None) – If not None (default), count only those member nodes with the specified degree.

Return type:

dict

See also

order

Examples

>>> import xgi
>>> H = xgi.Hypergraph([[1, 2, 3], [2, 3, 4, 5], [3, 4, 5]])
>>> H.edges.size.asdict()
{0: 3, 1: 4, 2: 3}

xgi.stats.edgestats.node_edge_centrality(net, bunch, f=<function <lambda>>, g=<function <lambda>>, phi=<function <lambda>>, psi=<function <lambda>>, max_iter=100, tol=1e-06)[source]

Computes edge centralities.

Parameters:

net (Hypergraph) – The hypergraph of interest
bunch (Iterable) – Edges in net
f (lambda function, default: x^2) – The function f as described in Tudisco and Higham. Must accept a numpy array.
g (lambda function, default: x^0.5) – The function g as described in Tudisco and Higham. Must accept a numpy array.
phi (lambda function, default: x^2) – The function phi as described in Tudisco and Higham. Must accept a numpy array.
psi (lambda function, default: x^0.5) – The function psi as described in Tudisco and Higham. Must accept a numpy array.
max_iter (int, default: 100) – Number of iterations at which the algorithm terminates if convergence is not reached.
tol (float > 0, default: 1e-6) – The total allowable error in the node and edge centralities.

Returns:

The edge centrality where keys are the edge IDs and values are associated centralities.

Return type:

dict, dict

Notes

In the paper from which this was taken, it is more general in that it includes general functions for both nodes and edges, nodes and edges may be weighted, and one can choose different norms for normalization.

This method does not output the node centralities even though they are computed.

References

Node and edge nonlinear eigenvector centrality for hypergraphs, Francesco Tudisco & Desmond J. Higham, https://doi.org/10.1038/s42005-021-00704-2