The Brain as a Complex System: Using Network Science as a Tool for Understanding the Brain

Abstract

Although graph theory has been around since the 18th century, the field of network science is more recent and continues to gain popularity, particularly in the field of neuroimaging. The field was propelled forward when Watts and Strogatz introduced their small-world network model, which described a network that provided regional specialization with efficient global information transfer. This model is appealing to the study of brain connectivity, as the brain can be viewed as a system with various interacting regions that produce complex behaviors. In practice, graph metrics such as clustering coefficient, path length, and efficiency measures are often used to characterize system properties. Centrality metrics such as degree, betweenness, closeness, and eigenvector centrality determine critical areas within the network. Community structure is also essential for understanding network organization and topology. Network science has led to a paradigm shift in the neuroscientific community, but it should be viewed as more than a simple ''tool du jour.'' To fully appreciate the utility of network science, a greater understanding of how network models apply to the brain is needed. An integrated appraisal of multiple network analyses should be performed to better understand network structure rather than focusing on univariate comparisons to find significant group differences; indeed, such comparisons, popular with traditional functional magnetic resonance imaging analyses, are arguably no longer relevant with graph-theory based approaches. These methods necessitate a philosophical shift toward complexity science. In this context, when correctly applied and interpreted, network scientific methods have a chance to revolutionize the understanding of brain function.

Functional brain networks: great expectations, hard times and the big leap forward

“…Significant differences in graph metrics can highlight differences between groups, but incur problems related to multiple comparisons. More importantly, they lead to dramatic information losses as a result of the reduction of a complex system to a set of scalars [9]. In addition, the standard statistical analysis does not provide a principled way to favour one property over another, neither does it account for the relationship between different metrics, which remains unexplored.…”

Resting state connectivity patterns with near-infrared spectroscopy data of the whole head

“…Indeed, complex systems' tools have been successfully employed to neuroimaging data recently, which has allowed researchers to explore intrinsic features of the brain. Of major interest in the literature is the brain's functional interaction between different regions, which can be investigated with graph theory approaches [1][2][3][4]. Recent studies from Blood Oxygen Level Dependent (BOLD) functional Magnetic Resonance Imaging (fMRI) has presented remarkable features of brain networks, such as highly connected hubs [5], hierarchy [6], assortativity [6,7], and small-worldness [8].…”

Bayesian exponential random graph modeling of whole-brain structural networks across lifespan

“…Fourthly, graph analysis consists of univariable comparisons (i.e., network metrics are determined independent from each other) due to lack of a unifying framework (Telesford et al, 2011). However, many metrics are highly correlated and non-exclusive (Bounova and De Weck, 2012;Meghanathan, 2015).…”