SmallWorld

class brainpy.connect.SmallWorld(num_neighbor, prob, directed=False, include_self=False, seed=None, **kwargs)

Build a Watts–Strogatz small-world graph.

Parameters:

• num_neighbor (int) – Each node is joined with its k nearest neighbors in a ring topology.

• prob (float) – The probability of rewiring each edge

• directed (bool) – Whether the graph is a directed graph.

• include_self (bool) – Whether include the node self.

Notes

First create a ring over \(num\_node\) nodes [1]. Then each node in the ring is joined to its \(num\_neighbor\) nearest neighbors (or \(num\_neighbor - 1\) neighbors if \(num\_neighbor\) is odd). Then shortcuts are created by replacing some edges as follows: for each edge \((u, v)\) in the underlying “\(num\_node\)-ring with \(num\_neighbor\) nearest neighbors” with probability \(prob\) replace it with a new edge \((u, w)\) with uniformly random choice of existing node \(w\).

References

[1]

Duncan J. Watts and Steven H. Strogatz, Collective dynamics of small-world networks, Nature, 393, pp. 440–442, 1998.

build_conn()

build connections with certain data type.

If users want to customize their connections, please provide one of the following functions:

• build_mat(): build a matrix binary connection matrix.

• build_csr(): build a csr sparse connection data.

• build_coo(): build a coo sparse connection data.

• build_conn(): deprecated.

Returns:

conn – A tuple with two elements: connection type (str) and connection data. For example: return 'csr', (ind, indptr) Or a dict with three elements: csr, mat and coo. For example: return dict(csr=(ind, indptr), mat=None, coo=None)

Return type:

tuple, dict