IEEE Signal Processing - May 2018 - 88

Provincial
Node

Edge

Connector
(a)

(b)

(c)

(d)

FIGURE 3. Some metrics used in undirected graphs built from connectivity methods applied to brain sources reconstructed from EEG. (a) Degree: A node
with high degree compared to other nodes. (b) Clustering coefficient: The clustering coefficient of a node is computed as the number of triangles attached
to a node, relative to the total possible number of triangles. (c) Shortest path length: The shortest path between two nodes. The characteristic path length
of a network is the average path length between every pair of nodes. (d) Modularity: An illustration of a modular decomposition of the network. Two modules have been identified, as represented by the different background colors. Nodes within a module are strongly connected with each other and sparsely
connected with nodes in other modules. Such decomposition allows for analysis of node roles and hub category. A provincial hub is highly connected
within its own module, while a connector hub has connections distributed across modules.

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segregation in networks. The more the neighborhood of
node i is densely interconnected, the higher is its local
clustering coefficient. This network measure will be used
in a real application described next (Figure 4).
The path length is the average weighted shortest path length
often used as a measure for the global integration of the network. It is defined as the harmonic average of the shortest
paths between all possible vertex pairs in the network,
where the shortest path between two vertices is defined as
the path with the largest total weight.
The global efficiency E G of a network is the inverse of the
characteristic path length. Several studies have used E G as
a measure of information processing capability. The global
efficiency is a measure of integrated and parallel information processing [Figure 3(c)].
Generally speaking, in a network, the functional value of
a node is proportional to the number of paths in which it
participates. A way to find the critical nodes in a brain
network is to calculate the betweenness centrality of each
node. This value is defined as the number of shortest
paths in the network that pass through the node normalized by the total number of shortest paths.
Another metric used to characterize network topology is
modularity, which denotes the partitioning of the associated graph into clusters or modules (also called communities). A network module is defined as a subset of nodes
in the graph that are more densely connected to other
nodes within the same module than to the nodes in the
other modules.
Hubness can be measured based on the intramodular connectivity Z and participation coefficient PC. Once the modularity is calculated and optimal modules have been identified,
the Z and PC metrics are computed for each node. The
nodes are classified as hubs if their Z is higher than a defined
threshold T; otherwise, they are classified as nonhubs.
Using PC, a hub can be classified as a provincial hub, where
the nodes are mostly connected to nodes within its own module, or as a connector hub, where the nodes have diverse

connectivity across several different modules in the network
[Figure 3(d)]. For dynamic networks, the modularity can
be computed using the multislice network modularity
algorithm [32].

Software
Several software packages have been developed to process
EEG signals, such as EEGLAB, CARTOOL, Fieldtrip, and
Brainstorm. In addition, various toolboxes have been proposed to
analyze and visualize complex networks, such as the Brain
Connectivity Toolbox (BCT), BrainNet Viewer (BNV), the
GCCA toolbox, the Connectome Mapper, Gephi, the Connectome Viewer, eConnectome, EEGNET, the Connectome
Visualization Utility, and GraphVar. However, a comprehensive
tool that implements the complete pipeline from EEG processing to analysis and visualization of brain networks is still missing. Table 1 provides a list of MATLAB-based tools, along with
their main functionalities in terms of EEG preprocessing and
inverse solutions, functional and effective connectivity measures,
and network characterization and visualization.

Dynamic reconfiguration of functional brain networks
Tracking the temporal dynamics of brain networks is an issue of
great interest in cognition and neuropathology. The term brain
network reconfiguration refers to slow changes across a lifetime
due to experiences and to rapid spontaneous or evoked changes
in response to external stimuli or perturbations [33]. For
instance, an important challenge is to temporally follow, over a
subsecond-level time duration, changes in functional brain networks involved in a cognitive task. A key advantage of EEG is
its excellent temporal resolution, which offers the unique opportunity to track large-scale brain networks over time. This outstanding temporal resolution permits the analysis of the dynamic
properties of brain processes, an issue so far addressed in only a
few studies dealing with cognitive activity or with the resting
state (where participants are not involved in a particular task).
Many studies have reported that some brain regions remain
highly functionally connected even when subjects are at rest

IEEE Signal Processing Magazine

May 2018

Table of Contents for the Digital Edition of IEEE Signal Processing - May 2018