`connectivity`¶

Functions for determining network connectivity properties.

pyphi.connectivity.apply_boundary_conditions_to_cm(external_indices, cm)¶: Remove connections to or from external nodes.

pyphi.connectivity.get_inputs_from_cm(index, cm)¶: Return indices of inputs to the node with the given index.

pyphi.connectivity.get_outputs_from_cm(index, cm)¶: Return indices of the outputs of node with the given index.

pyphi.connectivity.causally_significant_nodes(cm)¶: Return indices of nodes that have both inputs and outputs.

pyphi.connectivity.relevant_connections(n, _from, to)¶

Construct a connectivity matrix.

Parameters:	n (int) – The dimensions of the matrix _from (tuple[int]) – Nodes with outgoing connections to `to` to (tuple[int]) – Nodes with incoming connections from `_from`
Returns:	An \(N \times N\) connectivity matrix with the \((i,j)^{\textrm{th}}\) entry is `1` if \(i\) is in `_from` and \(j\) is in `to`, and 0 otherwise.
Return type:	np.ndarray

pyphi.connectivity.block_cm(cm)¶

Return whether cm can be arranged as a block connectivity matrix.

If so, the corresponding mechanism/purview is trivially reducible. Technically, only square matrices are “block diagonal”, but the notion of connectivity carries over.

We test for block connectivity by trying to grow a block of nodes such that:

‘source’ nodes only input to nodes in the block
‘sink’ nodes only receive inputs from source nodes in the block

For example, the following connectivity matrix represents connections from nodes1 = A, B, C to nodes2 = D, E, F, G (without loss of generality, note that nodes1 and nodes2 may share elements):

   D  E  F  G
A [1, 1, 0, 0]
B [1, 1, 0, 0]
C [0, 0, 1, 1]

Since nodes \(AB\) only connect to nodes \(DE\), and node \(C\) only connects to nodes \(FG\), the subgraph is reducible, because the cut

A,B    C
─── ✕ ───
D,E   F,G

does not change the structure of the graph.

pyphi.connectivity.block_reducible(cm, nodes1, nodes2)¶

Return whether connections from nodes1 to nodes2 are reducible.

Parameters:	cm (np.ndarray) – The network’s connectivity matrix. nodes1 (tuple[int]) – Source nodes nodes2 (tuple[int]) – Sink nodes

pyphi.connectivity.is_strong(cm, nodes=None)¶

Return whether the connectivity matrix is strongly connected.

Remember that a singleton graph is strongly connected.

Keyword Arguments:
Parameters:	cm (np.ndarray) – A square connectivity matrix.
	nodes (tuple[int]) – A subset of nodes to consider.

pyphi.connectivity.is_weak(cm, nodes=None)¶

Return whether the connectivity matrix is weakly connected.

Keyword Arguments:
Parameters:	cm (np.ndarray) – A square connectivity matrix.
	nodes (tuple[int]) – A subset of nodes to consider.

pyphi.connectivity.is_full(cm, nodes1, nodes2)¶

Test connectivity of one set of nodes to another.

Parameters:	cm (`np.ndarrray`) – The connectivity matrix nodes1 (tuple[int]) – The nodes whose outputs to `nodes2` will be tested. nodes2 (tuple[int]) – The nodes whose inputs from `nodes1` will be tested.
Returns:	`True` if all elements in `nodes1` output to some element in `nodes2` and all elements in `nodes2` have an input from some element in `nodes1`, or if either set of nodes is empty; `False` otherwise.
Return type:	bool

connectivity¶

`connectivity`¶