9

Complex Brain Networks: A

Graph-Theoretical Analysis

Kayhan Erciyes

Maltepe University, İstanbul, Türkiye

Complex brain networks are large consisting of many functional nodes and

many more connections between them. A complex brain network may be

modeled by a graph enabling many results obtained in this field of mathe-

matics to be applied to the analysis of these networks. The nodes in a graph

representing a brain network denote regions of the brain and edges show the

structural or functional connections between these regions. In this review, we

first describe how to construct various brain networks from data obtained by

neuroimaging methods. We then review the analysis processes of graphs rep-

resenting brain networks and focus on three main areas of research in brain

networks: module detection to find clusters in brain networks, motif search

to detect frequent repeating subgraphs and network alignment to evaluate

similarities between two or more brain networks. We also provide a review of

brain network alterations in various neurological disorders.

9.1

Introduction

Analysis of the brain has been an active research area due to three main ad-

vancements in the last decades: advancement in neuroimaging technologies,

development of high-performance computers and development of software, al-

gorithms and methods to analyze data obtained from various neuroimaging

processes [1] which may be visualized as a graph with nodes and edges con-

necting the nodes.

Complex networks are large, consisting of thousands of nodes and tens of

thousands of edges between these nodes. These networks range from biological

networks to the Internet and to social networks. Analysis of these seemingly

DOI: 10.1201/9781003461906-9

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