Complex Brain Networks: A Graph-Theoretical Analysis

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diverse networks shows that they have some common characteristics not found

in randomly constructed networks of similar sizes. Firstly, distance between

any two nodes in a complex network is small compared to the number of nodes

and this effect is called small-world property. Another frequently observed

structure in complex networks is the manifestation of very few nodes with high

number of connections where the rest of the nodes have fewer connections in

general, termed as scale-free feature. Brain networks are a class of complex

networks exhibiting the aforementioned small-world and scale-free properties,

moreover, hierarchical cluster structures are also present in these networks.

In this review, we first describe the construction of various brain networks

using data from neuroimaging techniques. We then review fundamental large

graph analysis parameters and then concentrate on three main areas of brain

network analysis: module detection or clustering, network motif search, and

network alignment. We also investigate the relationship between brain net-

works and diseases of the brain with emphasis on the alterations of the brain

networks due to neurological disorders. We conclude by reviewing the benefits

of using graph theory as a tool to investigate brain networks to understand

functioning of the brain in health and disease.

9.2

Brain Network Construction

The main neuroimaging technologies are functional magnetic resonance imag-

ing (fMRI), diffusion tensor imaging (DTI), and electroencephalography

(EEG) which may be utilized effectively to build brain networks. Difficulty of

building a network of neuron nodes and interactions between them only en-

tails dividing the brain into coarser areas called region of interest (ROI) with

edges representing the communication between the ROIs. Types of networks

produced by various neuroimaging methods are as follows [1]:

• Structural Brain Networks: This type of brain network, is formed using neu-

ron synaptic connections and tracks that connect a cluster of neurons to

another cluster. Brain networks obtained this way are called structural brain

networks (SBN). Structure of a SBN is stable with changes in time scales of

seconds or minutes.

• Functional Brain Networks (FBN): This brain network is constructed using

fMRI data which is obtained by evaluating the blood-oxygen-level-dependent

(BOLD) signal that shows the neural activity in a brain region.

• Morphological Brain Networks (MBN): The morphological brain networks

consider the size, the shape and structure of brain regions such as cortical

thickness or grey matter volume, rather than the functions performed by

them. Commonly, average cortical values are calculated for each region and