This example computes the all-to-all connectivity between 68 regions in source space based on dSPM inverse solutions and a FreeSurfer cortical parcellation. The connectivity is visualized using a circular graph which is ordered based on the locations of the regions.

Out:

```
Reading inverse operator decomposition from /home/ubuntu/mne_data/MNE-sample-data/MEG/sample/sample_audvis-meg-oct-6-meg-inv.fif...
Reading inverse operator info...
[done]
Reading inverse operator decomposition...
[done]
305 x 305 full covariance (kind = 1) found.
Read a total of 4 projection items:
PCA-v1 (1 x 102) active
PCA-v2 (1 x 102) active
PCA-v3 (1 x 102) active
Average EEG reference (1 x 60) active
Noise covariance matrix read.
22494 x 22494 diagonal covariance (kind = 2) found.
Source covariance matrix read.
22494 x 22494 diagonal covariance (kind = 6) found.
Orientation priors read.
22494 x 22494 diagonal covariance (kind = 5) found.
Depth priors read.
Did not find the desired covariance matrix (kind = 3)
Reading a source space...
Computing patch statistics...
Patch information added...
Distance information added...
[done]
Reading a source space...
Computing patch statistics...
Patch information added...
Distance information added...
[done]
2 source spaces read
Read a total of 4 projection items:
PCA-v1 (1 x 102) active
PCA-v2 (1 x 102) active
PCA-v3 (1 x 102) active
Average EEG reference (1 x 60) active
Source spaces transformed to the inverse solution coordinate frame
Opening raw data file /home/ubuntu/mne_data/MNE-sample-data/MEG/sample/sample_audvis_filt-0-40_raw.fif...
Read a total of 4 projection items:
PCA-v1 (1 x 102) idle
PCA-v2 (1 x 102) idle
PCA-v3 (1 x 102) idle
Average EEG reference (1 x 60) idle
Range : 6450 ... 48149 = 42.956 ... 320.665 secs
Ready.
Current compensation grade : 0
72 matching events found
Created an SSP operator (subspace dimension = 3)
4 projection items activated
Reading labels from parcellation..
read 34 labels from /home/ubuntu/mne_data/MNE-sample-data/subjects/sample/label/lh.aparc.annot
read 34 labels from /home/ubuntu/mne_data/MNE-sample-data/subjects/sample/label/rh.aparc.annot
[done]
Connectivity computation...
Preparing the inverse operator for use...
Scaled noise and source covariance from nave = 1 to nave = 1
Created the regularized inverter
Created an SSP operator (subspace dimension = 3)
Created the whitener using a full noise covariance matrix (3 small eigenvalues omitted)
Computing noise-normalization factors (dSPM)...
[done]
Picked 305 channels from the data
Computing inverse...
(eigenleads need to be weighted)...
Processing epoch : 1
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for 2278 connections
using t=0.000s..0.699s for estimation (106 points)
frequencies: 8.5Hz..12.7Hz (4 points)
connectivity scores will be averaged for each band
using multitaper spectrum estimation with 7 DPSS windows
the following metrics will be computed: PLI, Debiased WPLI Square
computing connectivity for epoch 1
Processing epoch : 2
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 2
Processing epoch : 3
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 3
Processing epoch : 4
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 4
Processing epoch : 5
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 5
Processing epoch : 6
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 6
Processing epoch : 7
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 7
Processing epoch : 8
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 8
Processing epoch : 9
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 9
Processing epoch : 10
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 10
Rejecting epoch based on EOG : [u'EOG 061']
Processing epoch : 11
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 11
Processing epoch : 12
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 12
Processing epoch : 13
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 13
Rejecting epoch based on EOG : [u'EOG 061']
Rejecting epoch based on EOG : [u'EOG 061']
Processing epoch : 14
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 14
Processing epoch : 15
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 15
Processing epoch : 16
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 16
Processing epoch : 17
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 17
Rejecting epoch based on EOG : [u'EOG 061']
Processing epoch : 18
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 18
Processing epoch : 19
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 19
Processing epoch : 20
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 20
Rejecting epoch based on EOG : [u'EOG 061']
Processing epoch : 21
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 21
Processing epoch : 22
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 22
Processing epoch : 23
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 23
Rejecting epoch based on MAG : [u'MEG 1711']
Processing epoch : 24
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 24
Processing epoch : 25
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 25
Processing epoch : 26
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 26
Processing epoch : 27
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 27
Processing epoch : 28
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 28
Rejecting epoch based on EOG : [u'EOG 061']
Processing epoch : 29
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 29
Processing epoch : 30
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 30
Processing epoch : 31
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 31
Rejecting epoch based on EOG : [u'EOG 061']
Processing epoch : 32
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 32
Processing epoch : 33
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 33
Rejecting epoch based on EOG : [u'EOG 061']
Processing epoch : 34
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 34
Processing epoch : 35
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 35
Rejecting epoch based on EOG : [u'EOG 061']
Rejecting epoch based on EOG : [u'EOG 061']
Processing epoch : 36
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 36
Rejecting epoch based on EOG : [u'EOG 061']
Rejecting epoch based on EOG : [u'EOG 061']
Processing epoch : 37
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 37
Processing epoch : 38
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 38
Processing epoch : 39
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 39
Processing epoch : 40
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 40
Processing epoch : 41
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 41
Processing epoch : 42
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 42
Processing epoch : 43
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 43
Processing epoch : 44
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 44
Rejecting epoch based on EOG : [u'EOG 061']
Processing epoch : 45
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 45
Rejecting epoch based on EOG : [u'EOG 061']
Processing epoch : 46
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 46
Processing epoch : 47
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 47
Processing epoch : 48
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 48
Rejecting epoch based on EOG : [u'EOG 061']
Rejecting epoch based on EOG : [u'EOG 061']
Processing epoch : 49
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 49
Processing epoch : 50
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 50
Processing epoch : 51
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 51
Processing epoch : 52
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 52
Processing epoch : 53
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 53
Processing epoch : 54
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 54
Processing epoch : 55
Extracting time courses for 68 labels (mode: mean_flip)
computing connectivity for epoch 55
[done]
assembling connectivity matrix
[Connectivity computation done]
```

```
# Authors: Martin Luessi <mluessi@nmr.mgh.harvard.edu>
# Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
# Nicolas P. Rougier (graph code borrowed from his matplotlib gallery)
#
# License: BSD (3-clause)
import numpy as np
import matplotlib.pyplot as plt
import mne
from mne.datasets import sample
from mne.minimum_norm import apply_inverse_epochs, read_inverse_operator
from mne.connectivity import spectral_connectivity
from mne.viz import circular_layout, plot_connectivity_circle
print(__doc__)
data_path = sample.data_path()
subjects_dir = data_path + '/subjects'
fname_inv = data_path + '/MEG/sample/sample_audvis-meg-oct-6-meg-inv.fif'
fname_raw = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw.fif'
fname_event = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw-eve.fif'
# Load data
inverse_operator = read_inverse_operator(fname_inv)
raw = mne.io.read_raw_fif(fname_raw)
events = mne.read_events(fname_event)
# Add a bad channel
raw.info['bads'] += ['MEG 2443']
# Pick MEG channels
picks = mne.pick_types(raw.info, meg=True, eeg=False, stim=False, eog=True,
exclude='bads')
# Define epochs for left-auditory condition
event_id, tmin, tmax = 1, -0.2, 0.5
epochs = mne.Epochs(raw, events, event_id, tmin, tmax, picks=picks,
baseline=(None, 0), reject=dict(mag=4e-12, grad=4000e-13,
eog=150e-6))
# Compute inverse solution and for each epoch. By using "return_generator=True"
# stcs will be a generator object instead of a list.
snr = 1.0 # use lower SNR for single epochs
lambda2 = 1.0 / snr ** 2
method = "dSPM" # use dSPM method (could also be MNE or sLORETA)
stcs = apply_inverse_epochs(epochs, inverse_operator, lambda2, method,
pick_ori="normal", return_generator=True)
# Get labels for FreeSurfer 'aparc' cortical parcellation with 34 labels/hemi
labels = mne.read_labels_from_annot('sample', parc='aparc',
subjects_dir=subjects_dir)
label_colors = [label.color for label in labels]
# Average the source estimates within each label using sign-flips to reduce
# signal cancellations, also here we return a generator
src = inverse_operator['src']
label_ts = mne.extract_label_time_course(stcs, labels, src, mode='mean_flip',
return_generator=True)
# Now we are ready to compute the connectivity in the alpha band. Notice
# from the status messages, how mne-python: 1) reads an epoch from the raw
# file, 2) applies SSP and baseline correction, 3) computes the inverse to
# obtain a source estimate, 4) averages the source estimate to obtain a
# time series for each label, 5) includes the label time series in the
# connectivity computation, and then moves to the next epoch. This
# behaviour is because we are using generators and allows us to
# compute connectivity in computationally efficient manner where the amount
# of memory (RAM) needed is independent from the number of epochs.
fmin = 8.
fmax = 13.
sfreq = raw.info['sfreq'] # the sampling frequency
con_methods = ['pli', 'wpli2_debiased']
con, freqs, times, n_epochs, n_tapers = spectral_connectivity(
label_ts, method=con_methods, mode='multitaper', sfreq=sfreq, fmin=fmin,
fmax=fmax, faverage=True, mt_adaptive=True, n_jobs=1)
# con is a 3D array, get the connectivity for the first (and only) freq. band
# for each method
con_res = dict()
for method, c in zip(con_methods, con):
con_res[method] = c[:, :, 0]
# Now, we visualize the connectivity using a circular graph layout
# First, we reorder the labels based on their location in the left hemi
label_names = [label.name for label in labels]
lh_labels = [name for name in label_names if name.endswith('lh')]
# Get the y-location of the label
label_ypos = list()
for name in lh_labels:
idx = label_names.index(name)
ypos = np.mean(labels[idx].pos[:, 1])
label_ypos.append(ypos)
# Reorder the labels based on their location
lh_labels = [label for (yp, label) in sorted(zip(label_ypos, lh_labels))]
# For the right hemi
rh_labels = [label[:-2] + 'rh' for label in lh_labels]
# Save the plot order and create a circular layout
node_order = list()
node_order.extend(lh_labels[::-1]) # reverse the order
node_order.extend(rh_labels)
node_angles = circular_layout(label_names, node_order, start_pos=90,
group_boundaries=[0, len(label_names) / 2])
# Plot the graph using node colors from the FreeSurfer parcellation. We only
# show the 300 strongest connections.
plot_connectivity_circle(con_res['pli'], label_names, n_lines=300,
node_angles=node_angles, node_colors=label_colors,
title='All-to-All Connectivity left-Auditory '
'Condition (PLI)')
plt.savefig('circle.png', facecolor='black')
# Plot connectivity for both methods in the same plot
fig = plt.figure(num=None, figsize=(8, 4), facecolor='black')
no_names = [''] * len(label_names)
for ii, method in enumerate(con_methods):
plot_connectivity_circle(con_res[method], no_names, n_lines=300,
node_angles=node_angles, node_colors=label_colors,
title=method, padding=0, fontsize_colorbar=6,
fig=fig, subplot=(1, 2, ii + 1))
plt.show()
```

**Total running time of the script:** ( 0 minutes 7.882 seconds)