Tutorial 3: The connectivity matrix¶

Viewing the connectivity matrix is another way of examining the networks within the brain, complementing other methods.

In these visualizations a node x node matrix shows the connectivity values.

To view a connectivity matrix for your nextwork, simply set a view argument to "c".

NetPlotBrain enables you to effortlessly generate a connectivity matrix alongside the brain, along with a few extra features.

Generating data¶

So let us generate some normally distributed data to use as our connectivity matrix.

In [1]:

import numpy as np
import itertools
import pandas as pd
import netplotbrain

import numpy as np import itertools import pandas as pd import netplotbrain

In [2]:

mu = np.zeros(30)
sigma = np.eye(30)
# Set within network connectivity
i, j = list(zip(*itertools.combinations(np.arange(0, 10), 2)))
sigma[i, j] = 0.7
i, j = list(zip(*itertools.combinations(np.arange(10, 20), 2)))
sigma[i, j] = 0.7
i, j = list(zip(*itertools.combinations(np.arange(20, 30), 2)))
sigma[i, j] = 0.6
# Set between network connectivity
sigma[20:][:, :20] = -0.2
sigma[10:20][:, :10] = 0.1
sigma = sigma + sigma.T
np.fill_diagonal(sigma, 1)
# Generate the random data
np.random.seed(42)
data = np.random.multivariate_normal(mu, sigma, 1000)

mu = np.zeros(30) sigma = np.eye(30) # Set within network connectivity i, j = list(zip(*itertools.combinations(np.arange(0, 10), 2))) sigma[i, j] = 0.7 i, j = list(zip(*itertools.combinations(np.arange(10, 20), 2))) sigma[i, j] = 0.7 i, j = list(zip(*itertools.combinations(np.arange(20, 30), 2))) sigma[i, j] = 0.6 # Set between network connectivity sigma[20:][:, :20] = -0.2 sigma[10:20][:, :10] = 0.1 sigma = sigma + sigma.T np.fill_diagonal(sigma, 1) # Generate the random data np.random.seed(42) data = np.random.multivariate_normal(mu, sigma, 1000)

In [3]:

# Create connectivity matrix
cm = pd.DataFrame(data).corr().values
# Here we see we have created a 30 x 30 matrix
cm.shape

# Create connectivity matrix cm = pd.DataFrame(data).corr().values # Here we see we have created a 30 x 30 matrix cm.shape

Out[3]:

(30, 30)

In [4]:

# Plot the connectivity matrix
netplotbrain.plot(edges=cm,
                  view='c')

# Plot the connectivity matrix netplotbrain.plot(edges=cm, view='c')

Out[4]:

(<Figure size 216x216 with 1 Axes>, [<Axes: >])

Shuffling up the order¶

Now multiple different options can be specified. One such opttion is the order of the nodes. Here the nodes are already ordered, but this is not always the case.

In [5]:

random_order = np.random.permutation(np.arange(30))
cm = cm[random_order][:, random_order]
netplotbrain.plot(edges=cm, view='c')

# + [markdown]
# ### cm_order can set the order of nodes.

random_order = np.random.permutation(np.arange(30)) cm = cm[random_order][:, random_order] netplotbrain.plot(edges=cm, view='c') # + [markdown] # ### cm_order can set the order of nodes.

Out[5]:

(<Figure size 216x216 with 1 Axes>, [<Axes: >])

In [6]:

# cm_order is either a list of indicies or a list of communities
cm_order = np.argsort(random_order)
netplotbrain.plot(edges=cm, view='c', 
                  cm_order=cm_order)

# + [markdown]
# ### Turning of the rotated option

# cm_order is either a list of indicies or a list of communities cm_order = np.argsort(random_order) netplotbrain.plot(edges=cm, view='c', cm_order=cm_order) # + [markdown] # ### Turning of the rotated option

/home/xthowi/packages/netplotbrain/netplotbrain/plotting/plot_cm.py:33: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison
  if cm_order == 'auto' and node_colorby is not None:
/home/xthowi/packages/netplotbrain/netplotbrain/plotting/plot_cm.py:37: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison
  elif cm_order == 'auto':

Out[6]:

(<Figure size 216x216 with 1 Axes>, [<Axes: >])

In [7]:

netplotbrain.plot(edges=cm, view='c', 
                  cm_order=cm_order, 
                  cm_rotate=False)

# + [markdown]
# ### ringing in the community with node_color.

netplotbrain.plot(edges=cm, view='c', cm_order=cm_order, cm_rotate=False) # + [markdown] # ### ringing in the community with node_color.

/home/xthowi/packages/netplotbrain/netplotbrain/plotting/plot_cm.py:33: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison
  if cm_order == 'auto' and node_colorby is not None:
/home/xthowi/packages/netplotbrain/netplotbrain/plotting/plot_cm.py:37: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison
  elif cm_order == 'auto':

Out[7]:

(<Figure size 216x216 with 1 Axes>, [<Axes: >])

In [8]:

# Lets put cm back in its correct order
cm = cm[cm_order][:, cm_order]

# Load example nodes, take only xyz and first 30 rows
nodes = pd.read_csv(netplotbrain.__path__[0] + '/example_data/example_nodes.tsv', sep='\t', index_col=0)
nodes = nodes[['x', 'y', 'z']].iloc[:30]
# Add new community names
nodes['community_names'] = ['FP']*10 + ['SM']*10 + ['DMN']*10

# Lets put cm back in its correct order cm = cm[cm_order][:, cm_order] # Load example nodes, take only xyz and first 30 rows nodes = pd.read_csv(netplotbrain.__path__[0] + '/example_data/example_nodes.tsv', sep='\t', index_col=0) nodes = nodes[['x', 'y', 'z']].iloc[:30] # Add new community names nodes['community_names'] = ['FP']*10 + ['SM']*10 + ['DMN']*10

In [9]:

netplotbrain.plot(edges=cm, view='Sc', 
                  nodes=nodes, node_color='community_names', 
                  node_scale=50,
                  node_cmap='Set2',
                  title='Brain and connectivity mastrix sharing colors',
                  subtitles=None,
                  cm_boundarywidth=4,
                  cm_bordercolor = 'black',
                  cm_borderwidth = 2,
                  edge_color='lightgray',
                  edge_wights=0.1)

netplotbrain.plot(edges=cm, view='Sc', nodes=nodes, node_color='community_names', node_scale=50, node_cmap='Set2', title='Brain and connectivity mastrix sharing colors', subtitles=None, cm_boundarywidth=4, cm_bordercolor = 'black', cm_borderwidth = 2, edge_color='lightgray', edge_wights=0.1)

Out[9]:

(<Figure size 432x252 with 3 Axes>, [<Axes3D: >, <Axes: >, <Axes: >])

The above plot also shows the cm_boundarywidth argument which plots the width of the squares associated with node_color. It also show cm_borderwidth and cm_bordercolor which are the outside boundaries.