stats package

Statistics of networks, their nodes, and edges.

Any mapping that assigns some quantity to each node of a network is considered a node statistic. For example, the degree is a node-integer mapping, while a node attribute that assigns a string label to each node is a node-string mapping. The stats package provides a common interface to all such mappings.

Each such mapping is accessible via the H.nodes view. For example, the degree of all nodes supports type conversion using the as* methods.

>>> import xgi
>>> H = xgi.Hypergraph([[1, 2, 3], [2, 3, 4, 5], [3, 4, 5]])
>>> H.nodes.degree.asdict()
{1: 1, 2: 2, 3: 3, 4: 2, 5: 2}
>>> H.nodes.degree.aslist()
[1, 2, 3, 2, 2]

Another feature is the ability to filter the nodes of a network by degree.

>>> H.nodes.filterby('degree', 2)
NodeView((2, 4, 5))

The power of the stats package is that any other node statistic that can be conceived of as a node-quantity mapping is given the same interface. For example, node attributes get the same treatment:

>>> H.add_nodes_from([
...     (1, {"color": "red", "name": "horse"}),
...     (2, {"color": "blue", "name": "pony"}),
...     (3, {"color": "yellow", "name": "zebra"}),
...     (4, {"color": "red", "name": "orangutan", "age": 20}),
...     (5, {"color": "blue", "name": "fish", "age": 2}),
... ])
>>> H.nodes.attrs('color').asdict()
{1: 'red', 2: 'blue', 3: 'yellow', 4: 'red', 5: 'blue'}
>>> H.nodes.attrs('color').aslist()
['red', 'blue', 'yellow', 'red', 'blue']
>>> H.nodes.filterby_attr('color', 'red')
NodeView((1, 4))

Many other features are available, including edge-statistics, and user-defined statistics. For more details, see the tutorial.

Available statistics

Hypergraphs and simplicial complexes

Statistics of nodes

`average_neighbor_degree`	Average neighbor degree.
`clique_eigenvector_centrality`	Compute the clique motif eigenvector centrality of a hypergraph.
`clustering_coefficient`	Local clustering coefficient.
`degree`	Node degree.
`h_eigenvector_centrality`	Compute the H-eigenvector centrality of a hypergraph.
`local_clustering_coefficient`	Compute the local clustering coefficient.
`node_edge_centrality`	Computes node centralities.
`two_node_clustering_coefficient`	Return the clustering coefficients for each node in a Hypergraph.

Statistics of edges

`order`	Edge order.
`size`	Edge size.
`node_edge_centrality`	Computes edge centralities.

Corresponding decorators

`nodestat_func`	Decorate arbitrary functions to behave like `NodeStat` objects.
`edgestat_func`	Decorate arbitrary functions to behave like `EdgeStat` objects.

Corresponding modules

`nodestats`	Node statistics.
`edgestats`	Edge statistics.

Corresponding classes

`NodeStat`	An arbitrary node-quantity mapping.
`EdgeStat`	An arbitrary edge-quantity mapping.
`MultiNodeStat`	Multiple node-quantity mappings.
`MultiEdgeStat`	Multiple edge-quantity mappings.

Directed hypergraphs

Statistics of nodes

`degree`	Node degree.
`in_degree`	Node in-degree.
`out_degree`	Node out-degree.

Statistics of edges

`order`	Edge order.
`size`	Edge size.
`head_order`	Head order.
`head_size`	Head size.
`tail_order`	Tail order.
`tail_size`	Tail size.

Corresponding decorators

`dinodestat_func`	Decorator that allows arbitrary functions to behave like `DiNodeStat` objects.
`diedgestat_func`	Decorator that allows arbitrary functions to behave like `DiEdgeStat` objects.

Corresponding modules

`dinodestats`	Node statistics.
`diedgestats`	Directed edge statistics.

Corresponding classes

`DiNodeStat`	An arbitrary node-quantity mapping.
`DiEdgeStat`	An arbitrary edge-quantity mapping.
`MultiDiNodeStat`	Multiple node-quantity mappings.
`MultiDiEdgeStat`	Multiple edge-quantity mappings.