Brain Network Topology Analysis

Previous studies suggest that nicotine improves cognitive performance by changing the interaction between brain regions (Giessing et al., 2013). Thus, inter-individual differences in behavioural drug effects might be related to the baseline characteristics of brain networks before drug administration. Several studies suggest that efficient performance depends on the individual formation of processing pathways and the topology of large-scale brain networks (Wylie et al., 2012; Giessing et al., 2013). Therefore, a fundamental aspect to understand individual drug effects is to identify brain nodes that are central to propagate brain signals to a large portion of brain nodes (Newman, 2010; Malliaros et al., 2016). To investigate differences in nodal centrality between outliers and non-outliers, three measures of nodal centrality from graph theory were computed using the brain connectivity toolbox (Rubinov and Sporns, 2010; Fornito et al., 2016; Matas et al., 2017). As a first measure, “betweenness centrality” was calculated by the fraction of all shortest weighted paths in the network that contain a given node. Thus, nodes with high values of betweenness participate in a large number of shortest weighted paths between brain nodes. Second, we used the weighted undirected adjacency matrix to compute eigenvector centrality. Eigenvector centrality is a self-referential measure: the centrality score is proportional to the sum of the centrality scores of all nodes which are connected to it. Nodes get high eigenvector centrality if they are connected to other important nodes with high eigenvector centrality. If we aim the centralities to be non-negative, the eigenvector centrality of node i is equivalent to the ith element in the eigenvector corresponding to the largest eigenvalue of the adjacency matrix. As a last centrality measure, we computed the k-coreness of nodes to identify tightly interlinked groups within a network (Hagmann et al., 2008). To be part of the k-core of an undirected binary graph, a node has to be connected to at least k other nodes in the subgraph regardless of the connections to nodes outside this subgraph. The k-cores form a nested hierarchy, whereas nodes with highest k-coreness belong to the most interlinked, cohesive subgraph. For example, the three-core is the subset of nodes within the two-core that have at least three connections to all other members of the core. Thus, nodes with high k-coreness belong to tightly interlinked groups of nodes (Alvarez-Hamelin et al., 2005).

Comparing the different centrality measures, each measure gauges a slightly different aspect of node importance (Matas et al., 2017). Eigenvector centrality measures the connectedness of a node within a network; the eigenvector centrality of a node can be high because it is connected to many nodes or to nodes of high importance (or both). In contrast, “betweenness centrality” does not focus on the connectedness of a node, but how well a node controls flow between others by acting as a bridge along the shortest path between two other nodes. k-coreness is related to the propagation and spreading of information. The k-core decomposition progressively decomposes the networks in different layers revealing a nested structure of cores outmost to the most internal one. It has been shown that the nodes of the central core as identified by the k-shell decomposition analysis are most efficient in the spreading of information within the network. High efficient “spreaders” within the network do not necessarily correspond to the most highly connected nodes (Kitsak et al., 2010). In summary, the current analysis identifies different aspects of node centrality to investigate whether outliers and non-outliers differ in their most important nodes.

Within the network topology analyses, networks with equal edge densities were compared between outliers and non-outliers (see above). This was done to distinguish effects on network topology from effects on network density (van Wijk et al., 2010). However, due to the fixed number of edges, an increase of nodal connectedness in one brain region likely correlates with a decrease of centrality in a different region. This would lead to small averaged effects, despite possible systematic, but heterogeneous and non-uniform patterns of effects across nodes. To investigate heterogeneous effects, previous studies suggested to report sorted individual effects in an increasing order and indexed by percentiles (Chernozhukov et al., 2018). Within a first approach on the global level, we aimed to test whether these differences between outliers and non-outliers, either positive or negative changes, reflect systematic deviations over and above effects of noise. Using a randomisation approach, we tested whether the sum of the squared differences between outliers and non-outliers was significantly larger than expected under the null hypothesis. Within this randomisation approach, outlier and non-outliers were randomly intermixed for 5,000 times and for each randomisation the squared differences were computed to estimate the null distribution. In the following nodal analyses, the network density with the highest significance level within the global analysis was selected and for each individual node it was tested whether the investigated measures of centrality significantly differed between outliers and non-outliers.