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The integration and transmission of information in the brain are dependent on the interplay between structural and dynamical properties. Implicit in any pursuit aimed at understanding neural dynamics from appropriate sets of mathematically…
Understanding the evolution of brain functional networks over time is of great significance for the analysis of cognitive mechanisms and the diagnosis of neurological diseases. Existing methods often have difficulty in capturing the…
In this paper, we describe {\sc quantitative graph theory} and argue it is a new graph-theoretical branch in network science, however, with significant different features compared to classical graph theory. The main goal of quantitative…
Creating new ties in a social network facilitates knowledge exchange and affects positional advantage. In this paper, we study the process, which we call network building, of establishing ties between two existing social networks in order…
Cognition is supported by neurophysiological processes that occur both in local anatomical neighborhoods and in distributed large-scale circuits. Recent evidence from network control theory suggests that white matter pathways linking…
In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…
As networks continue to increase in size, current methods must be capable of handling large numbers of nodes and edges in order to be practically relevant. Instead of working directly with the entire (large) network, analyzing sub-networks…
The relationship between brain structure and function has been probed using a variety of approaches, but how the underlying structural connectivity of the human brain drives behavior is far from understood. To investigate the effect of…
The field of computational modeling of the brain is advancing so rapidly that now it is possible to model large scale networks representing different brain regions with a high level of biological detail in terms of numbers and synapses. For…
In the face of the stupefying complexity of the human brain, network analysis is a most useful tool that allows one to greatly simplify the problem, typically by approximating the billions of neurons comprising the brain by means of a…
Understanding brain connectivity in a network-theoretic context has shown much promise in recent years. This type of analysis identifies brain organisational principles, bringing a new perspective to neuroscience. At the same time, large…
Inferring a binary connectivity graph from resting-state fMRI data for a single subject requires making several methodological choices and assumptions that can significantly affect the results. In this study, we investigate the robustness…
There is increasing evidence to suggest functional connectivity networks are non-stationary. This has lead to the development of novel methodologies with which to accurately estimate time-varying functional connectivity networks. Many of…
Functional connectivity (FC) refers to the investigation of interactions between brain regions to understand integration of neural activity in several regions. FC is often estimated using functional magnetic resonance images (fMRI). There…
With recent advancements in non-invasive techniques for measuring brain activity, such as magnetic resonance imaging (MRI), the study of structural and functional brain networks through graph signal processing (GSP) has gained notable…
Data-driven brain parcellations aim to provide a more accurate representation of an individual's functional connectivity, since they are able to capture individual variability that arises due to development or disease. This renders…
The collection of data on populations of networks is becoming increasingly common, where each data point can be seen as a realisation of a network-valued random variable. A canonical example is that of brain networks: a typical neuroimaging…
The study of random networks in a neuroscientific context has developed extensively over the last couple of decades. By contrast, techniques for the statistical analysis of these networks are less developed. In this paper, we focus on the…
Networked systems display complex patterns of interactions between a large number of components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology,…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…