Stats Cheat Sheet#

Quick reference for XGI’s statistics interface. For a full tutorial, see Statistics.

Accessing stats#

Stats are accessed through the nodes and edges views:

import xgi
H = xgi.Hypergraph([[1, 2, 3], [2, 3, 4, 5], [3, 4, 5]])

H.nodes.degree            # NodeStat object
H.edges.order              # EdgeStat object

Output formats#

Every stat object supports the same output methods:

Method	Returns
`.asdict()`	`{id: value, ...}`
`.aslist()`	`[value, ...]`
`.asnumpy()`	NumPy array
`.aspandas()`	Pandas Series

Summary statistics#

Method	Description
`.max()`, `.min()`	Maximum / minimum value
`.mean()`, `.median()`, `.mode()`	Central tendency
`.std()`, `.var()`	Spread
`.sum()`	Total
`.moment(order, center)`	Statistical moments
`.argmax()`, `.argmin()`	ID of the max / min
`.argsort(reverse)`	IDs sorted by value
`.unique(return_counts)`	Unique values
`.ashist(bins, density)`	Histogram as DataFrame

Available node statistics#

Stat	Example
`degree`	`H.nodes.degree`
`average_neighbor_degree`	`H.nodes.average_neighbor_degree`
`clustering_coefficient`	`H.nodes.clustering_coefficient`
`local_clustering_coefficient`	`H.nodes.local_clustering_coefficient`
`two_node_clustering_coefficient`	`H.nodes.two_node_clustering_coefficient`
`clique_eigenvector_centrality`	`H.nodes.clique_eigenvector_centrality`
`h_eigenvector_centrality`	`H.nodes.h_eigenvector_centrality`
`z_eigenvector_centrality`	`H.nodes.z_eigenvector_centrality`
`node_edge_centrality`	`H.nodes.node_edge_centrality`
`katz_centrality`	`H.nodes.katz_centrality`
`attrs`	`H.nodes.attrs('color')`

Available edge statistics#

Stat	Example
`order`	`H.edges.order`
`size`	`H.edges.size`
`node_edge_centrality`	`H.edges.node_edge_centrality`
`attrs`	`H.edges.attrs('weight')`

Directed hypergraph statistics#

Nodes: degree, in_degree, out_degree

Edges: order, size, head_order, head_size, tail_order, tail_size

Passing arguments#

Some stats accept arguments. Call the stat to pass them:

H.nodes.degree              # all orders
H.nodes.degree(order=2)     # only order-2 edges
H.edges.order(degree=3)     # only nodes with degree 3

Filtering#

Filter nodes or edges by any statistic:

H.nodes.filterby('degree', 2)                      # degree == 2
H.nodes.filterby('degree', 2, mode='gt')           # degree > 2
H.nodes.filterby('degree', (2, 5), mode='between') # 2 <= degree <= 5
H.edges.filterby('order', 1, mode='leq')           # order <= 1

Available modes: eq, neq, lt, gt, leq, geq, between.

Filter by attributes:

H.nodes.filterby_attr('color', 'red')
H.nodes.filterby_attr('age', 18, mode='geq')

Multiple statistics#

Combine multiple stats into a single DataFrame:

H.nodes.multi(['degree', 'clustering_coefficient']).aspandas()

Custom statistics#

Define your own stats with decorators:

@xgi.nodestat_func
def my_stat(net, bunch):
    return {n: net.degree(n) ** 2 for n in bunch}

H.nodes.my_stat.asdict()  # works like any built-in stat

Using stats with visualization#

Pass stat objects directly to drawing functions:

xgi.draw(H, node_fc=H.nodes.degree, node_size=H.nodes.degree)
xgi.draw(H, edge_fc=H.edges.order)