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 into
, 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
tonodes2 = D, E, F, G
(without loss of generality, note thatnodes1
andnodes2
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
tonodes2
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.
Parameters: cm (np.ndarray) – A square connectivity matrix. Keyword Arguments: nodes (tuple[int]) – A subset of nodes to consider.

pyphi.connectivity.
is_weak
(cm, nodes=None)¶ Return whether the connectivity matrix is weakly connected.
Parameters: cm (np.ndarray) – A square connectivity matrix. Keyword Arguments: 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 innodes1
output to some element innodes2
and all elements innodes2
have an input from some element innodes1
, or if either set of nodes is empty;False
otherwise.Return type: bool
 cm (