braintools.analysis.graph.degree_distribution

braintools.analysis.graph.degree_distribution(conn, *, direction='in')

Compute node degrees and their histogram.

The graph is treated as directed and unweighted: the degree counts edges, not weights. Repeated pairs count once. A self-loop counts once in the in- and the out-degree and twice in the total degree, as in networkx.

Parameters:

• conn (Any) – Connectivity with rows as pre and columns as post neurons. It may be rectangular (pre and post populations of different sizes) for direction='in' or 'out'.

• direction (str) – 'in': number of incoming edges of each post neuron (column counts); 'out': outgoing edges of each pre neuron (row counts); 'total': their sum, as networkx.DiGraph.degree (needs a square connectivity).

Returns:

Named tuple (degrees, values, counts).

Return type:

DegreeDistribution

Raises:

ValueError – If direction is unknown, or 'total' is asked for a rectangular connectivity.

See also

clustering_coefficient

Local clustering of every node.

Notes

Host-only (NumPy/SciPy): not traceable by jax.jit, jax.vmap or jax.grad.

Examples

>>> import numpy as np
>>> from braintools.analysis.graph import degree_distribution
>>> adj = np.array([[0, 1, 1], [0, 0, 1], [0, 0, 0]])
>>> result = degree_distribution(adj, direction='in')
>>> result.degrees
array([0, 1, 2])
>>> result.counts
array([1, 1, 1])
>>>
>>> degree_distribution(adj, direction='total').degrees
array([2, 2, 2])
>>>
>>> self_loop = np.array([[1, 0], [1, 0]])  # 0 -> 0 and 1 -> 0
>>> degree_distribution(self_loop, direction='total').degrees
array([3, 1])