Minimum spanning tree analysis of the human connectome

Abstract

One of the challenges of brain network analysis is to directly compare network organization between subjects, irrespective of the number or strength of connections. In this study, we used minimum spanning tree (MST; a unique, acyclic subnetwork with a fixed number of connections) analysis to characterize the human brain network to create an empirical reference network. Such a reference network could be used as a null model of connections that form the backbone structure of the human brain. We analyzed the MST in three diffusion‐weighted imaging datasets of healthy adults. The MST of the group mean connectivity matrix was used as the empirical null‐model. The MST of individual subjects matched this reference MST for a mean 58%–88% of connections, depending on the analysis pipeline. Hub nodes in the MST matched with previously reported locations of hub regions, including the so‐called rich club nodes (a subset of high‐degree, highly interconnected nodes). Although most brain network studies have focused primarily on cortical connections, cortical–subcortical connections were consistently present in the MST across subjects. Brain network efficiency was higher when these connections were included in the analysis, suggesting that these tracts may be utilized as the major neural communication routes. Finally, we confirmed that MST characteristics index the effects of brain aging. We conclude that the MST provides an elegant and straightforward approach to analyze structural brain networks, and to test network topological features of individual subjects in comparison to empirical null models.

Functional brain networks in the schizophrenia spectrum and bipolar disorder with psychosis

“…To overcome these issues, the MST can be constructed, which is a subnetwork of the original graph that connects all nodes without forming loops and represents the network’s backbone 27 , 29 . The MST is relatively insensitive to differences in connectivity strength thereby enabling group comparisons of brain networks from different populations provided a similar number of nodes and a unique MST 29 , 65 .…”

fMRI network correlates of predisposing risk factors for delirium: A cross-sectional study

“…global functional connectivity strength, MST diameter, MST leaf fraction, PCC-DLPFC left and PCC-DLPFC right connectivity strength) were analyzed in separate linear regression models. As age, gender and IQ can be considered as confounders for delirium and network outcomes, we adjusted for center, age (if age was not the determinant), gender and IQ in the analyses ( Marcantonio, 2017 , Otte et al, 2015 , Stumme et al, 2020 , van Dellen et al, 2018 ). The associations of all seven risk factors combined on the five outcome measures, adjusted for center, gender and IQ, were studied with three different multivariable linear regression models.…”

Topological segregation of functional networks increases in developing brains

“…Subsequently, we reconstructed the minimum spanning tree (MST; Figure 1; Kruskal 1956; Wang et al 2008 ), so that the topology of functional networks could be characterised and compared without biases that are inherent in conventional graph theoretical approaches ( Stam, 2014; Tewarie et al, 2015 ). The MST is a sub-network that contains the strongest connections within a weighted network without forming cycles or loops; it provides an unbiased reconstruction of the core of a network, making it possible to create a unique backbone or empirical reference network (e.g., for large datasets such as the human brain connectome project; van Dellen et al 2018 ). Moreover, MST parameters are sensitive to alterations in the topology of brain networks at the functional- (e.g., Boersma et al 2013; de Bie et al 2012; Janssen et al 2017) and structural-level (e.g., Otte et al2015; van Dellen et al 2018 ), and importantly, can be interpreted along the lines of conventional graph theoretical measures ( Tewarie et al, 2016 ).…”