Multilayer¶

Multilayer graphs attach vertices and edges to elementary layer coordinates such as condition or time.

In [1]:

import annnet as an

import annnet as an

Define layers and supra-nodes¶

In [2]:

M = an.AnnNet(directed=False, aspects={'condition': ['ctrl', 'stim']})
M.add_vertices(['A', 'B'], layer=('ctrl',))
M.add_vertices(['A', 'B'], layer=('stim',))

print('aspects:', M.layers.list_aspects())
print('layers:', M.layers.list_layers())
print('global shape:', M.shape)

M = an.AnnNet(directed=False, aspects={'condition': ['ctrl', 'stim']}) M.add_vertices(['A', 'B'], layer=('ctrl',)) M.add_vertices(['A', 'B'], layer=('stim',)) print('aspects:', M.layers.list_aspects()) print('layers:', M.layers.list_layers()) print('global shape:', M.shape)

aspects: ('condition',)
layers: {'condition': ['ctrl', 'stim']}
global shape: (2, 0)

Intra-layer and coupling edges¶

In [3]:

M.add_edges(('A', ('ctrl',)), ('B', ('ctrl',)), edge_id='e_ctrl', weight=1.0)
M.add_edges(('A', ('stim',)), ('B', ('stim',)), edge_id='e_stim', weight=1.4)
n_couplings = M.layers.add_layer_coupling_pairs([(('ctrl',), ('stim',))])

print('coupling edges added:', n_couplings)
M.views.edges().select(['edge_id', 'kind', 'source', 'target', 'effective_weight'])

M.add_edges(('A', ('ctrl',)), ('B', ('ctrl',)), edge_id='e_ctrl', weight=1.0) M.add_edges(('A', ('stim',)), ('B', ('stim',)), edge_id='e_stim', weight=1.4) n_couplings = M.layers.add_layer_coupling_pairs([(('ctrl',), ('stim',))]) print('coupling edges added:', n_couplings) M.views.edges().select(['edge_id', 'kind', 'source', 'target', 'effective_weight'])

coupling edges added: 2

Out[3]:

shape: (4, 5)

edge_id	kind	source	target	effective_weight
str	str	str	str	f64
"e_ctrl"	"binary"	"('A', ('ctrl',))"	"('B', ('ctrl',))"	1.0
"e_stim"	"binary"	"('A', ('stim',))"	"('B', ('stim',))"	1.4
"A>A@ctrl~stim"	"binary"	"('A', ('ctrl',))"	"('A', ('stim',))"	1.0
"B>B@ctrl~stim"	"binary"	"('B', ('ctrl',))"	"('B', ('stim',))"	1.0

Draw the supra graph¶

Supra-nodes include both the base vertex and its layer coordinate, so the drawing makes coupling edges visible.

In [4]:

from annnet.utils import plotting

plotting.plot(M, backend='graphviz', show_edge_labels=True)

from annnet.utils import plotting plotting.plot(M, backend='graphviz', show_edge_labels=True)

Out[4]:

Layer selections and derived slices¶

In [5]:

stim_graph = M.layers.subgraph_from_layer_tuple(('stim',))
M.layers.create_slice_from_layer('stim_only', ('stim',))

print('stim graph shape:', stim_graph.shape)
print('stim slice edges:', sorted(M.slices.edges('stim_only')))

stim_graph = M.layers.subgraph_from_layer_tuple(('stim',)) M.layers.create_slice_from_layer('stim_only', ('stim',)) print('stim graph shape:', stim_graph.shape) print('stim slice edges:', sorted(M.slices.edges('stim_only')))

stim graph shape: (2, 1)
stim slice edges: ['e_stim']

Draw one layer as its own graph¶

In [6]:

plotting.plot(stim_graph, backend='graphviz', show_edge_labels=True)

plotting.plot(stim_graph, backend='graphviz', show_edge_labels=True)

Out[6]:

Supra matrices and a diffusion step¶

In [7]:

import numpy as np

adjacency = M.layers.supra_adjacency()
start = np.zeros(M.nv_supra)
start[0] = 1.0
diffused = M.layers.diffusion_step(start, tau=0.25)

print('supra-adjacency shape:', adjacency.shape)
print('supra-adjacency nnz:', adjacency.nnz)
print('diffused mass:', round(float(diffused.sum()), 3))

import numpy as np adjacency = M.layers.supra_adjacency() start = np.zeros(M.nv_supra) start[0] = 1.0 diffused = M.layers.diffusion_step(start, tau=0.25) print('supra-adjacency shape:', adjacency.shape) print('supra-adjacency nnz:', adjacency.nnz) print('diffused mass:', round(float(diffused.sum()), 3))

supra-adjacency shape: (4, 4)
supra-adjacency nnz: 8
diffused mass: 1.0

Multilayer AnnNet objects keep condition-specific topology, coupling edges, derived slices, and supra-level matrices in the same container.