21 Brain Morphological and Functional Networks …
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21.2.2 Brain Network Edge
In functional and morphological brain networks, edges are defined through an association matrix that captures relations (e.g. cross-correlation, mutual information etc.)
between nodal features. The matrix maps all possible pair-wise statistical associations between either regional morphological features or time series of their activity. For the purpose of estimation of network topological organization, these matrices can be binarised—mapping presence (and absence) of associations (edges); or
weighted—mapping strengths of association (edge strengths). There are differences
in approaches to analyse these networks. Binarised networks are analysed over a
range of binarisation thresholds to control for robustness and consistency of topological properties [5] and also for spurious/weak associations or noise [77]. Although
arbitrary by its nature, threshold is usually determined by network’s deviation from
random, null-model topology [60] and the presence of small-world and scale-free
topological properties [4]. Network edges can be weighted by the level (i.e., strength)
of association between nodal interactions. In functional networks, edges are weighted
by pair-wise temporal interactions, which are quantified either by correlation, coherence or synchronicity between time series [55]. In anatomical networks, the edges are
weighted by statistical associations (e.g., correlations) between different regional features: thickness, surface area, volume or curvature [3, 62, 79], usually across groups
of individuals.
Although neither functional nor morphological correlation networks are constructed on direct neural (axonal) connections between the regions involved, both
networks are largely constrained by underlying structural network [38]. For that reason, numerous studies have been focused on functional interactions that mirror the
local (segregated) brain anatomy and axonal links between such interactions [38].
However, the two networks organisations and their (within-networks) interactions
suggest complex, many-to-one function-structure mapping [32, 54]. Here, the focus
is on how the brain cytoarchitecture underpins these patterns of structural-functional
network associations. The relation between morphological and functional corticocortical connections, which are mapped by cytoarchitectonic and functional networks
is discussed in the Sect. 21.3.
21.2.3 Brain Network Modules
Modular topology is one ubiquitous characteristic of complex networks (including
the human brain). Networks can be divided into modules by grouping the densely
intra-connected sub-sets of nodes into a single sub-group (i.e., module). Algorithms
for the division of a (real-world) network into modules are usually optimized to allow
for sparse connections between groups (i.e., detection of overlapping communities)
[29, 52]. Furthermore, detecting modules in the network may help to identify those
nodes and their connections that may perform different functions with some degree of
333
21.2.2 Brain Network Edge
In functional and morphological brain networks, edges are defined through an association matrix that captures relations (e.g. cross-correlation, mutual information etc.)
between nodal features. The matrix maps all possible pair-wise statistical associations between either regional morphological features or time series of their activity. For the purpose of estimation of network topological organization, these matrices can be binarised—mapping presence (and absence) of associations (edges); or
weighted—mapping strengths of association (edge strengths). There are differences
in approaches to analyse these networks. Binarised networks are analysed over a
range of binarisation thresholds to control for robustness and consistency of topological properties [5] and also for spurious/weak associations or noise [77]. Although
arbitrary by its nature, threshold is usually determined by network’s deviation from
random, null-model topology [60] and the presence of small-world and scale-free
topological properties [4]. Network edges can be weighted by the level (i.e., strength)
of association between nodal interactions. In functional networks, edges are weighted
by pair-wise temporal interactions, which are quantified either by correlation, coherence or synchronicity between time series [55]. In anatomical networks, the edges are
weighted by statistical associations (e.g., correlations) between different regional features: thickness, surface area, volume or curvature [3, 62, 79], usually across groups
of individuals.
Although neither functional nor morphological correlation networks are constructed on direct neural (axonal) connections between the regions involved, both
networks are largely constrained by underlying structural network [38]. For that reason, numerous studies have been focused on functional interactions that mirror the
local (segregated) brain anatomy and axonal links between such interactions [38].
However, the two networks organisations and their (within-networks) interactions
suggest complex, many-to-one function-structure mapping [32, 54]. Here, the focus
is on how the brain cytoarchitecture underpins these patterns of structural-functional
network associations. The relation between morphological and functional corticocortical connections, which are mapped by cytoarchitectonic and functional networks
is discussed in the Sect. 21.3.
21.2.3 Brain Network Modules
Modular topology is one ubiquitous characteristic of complex networks (including
the human brain). Networks can be divided into modules by grouping the densely
intra-connected sub-sets of nodes into a single sub-group (i.e., module). Algorithms
for the division of a (real-world) network into modules are usually optimized to allow
for sparse connections between groups (i.e., detection of overlapping communities)
[29, 52]. Furthermore, detecting modules in the network may help to identify those
nodes and their connections that may perform different functions with some degree of