Estimating the impact of structural directionality: How reliable are undirected connectomes?

Abstract

Directionality is a fundamental feature of network connections. Most structural brain networks are intrinsically directed because of the nature of chemical synapses, which comprise most neuronal connections. Because of the limitations of noninvasive imaging techniques, the directionality of connections between structurally connected regions of the human brain cannot be confirmed. Hence, connections are represented as undirected, and it is still unknown how this lack of directionality affects brain network topology. Using six directed brain networks from different species and parcellations (cat, mouse, C. elegans, and three macaque networks), we estimate the inaccuracies in network measures (degree, betweenness, clustering coefficient, path length, global efficiency, participation index, and small-worldness) associated with the removal of the directionality of connections. We employ three different methods to render directed brain networks undirected: (a) remove unidirectional connections, (b) add reciprocal connections, and (c) combine equal numbers of removed and added unidirectional connections. We quantify the extent of inaccuracy in network measures introduced through neglecting connection directionality for individual nodes and across the network. We find that the coarse division between core and peripheral nodes remains accurate for undirected networks. However, hub nodes differ considerably when directionality is neglected. Comparing the different methods to generate undirected networks from directed ones, we generally find that the addition of reciprocal connections (false positives) causes larger errors in graph-theoretic measures than the removal of the same number of directed connections (false negatives). These findings suggest that directionality plays an essential role in shaping brain networks and highlight some limitations of undirected connectomes. Most brain networks are inherently directed because of the nature of chemical synapses, which comprise most neuronal connections. However, owing to limitations of non-invasive techniques, the human connectome is represented without directionality. To better understand the effects of directionality on graph-theoretic measures of anatomical networks, we compare brain networks across species when directionality is neglected, and find that hubs become vulnerable. Moreover, the addition of few false-positive reciprocal connections is more detrimental to network measures than the removal of the same number of directed false-negative connections. Our results suggest that directionality plays an essential role in shaping brain networks and highlight some limitations of undirected connectomes.

Keywords

• Directionality
• Connectome
• Structural connectivity
• Graph theory
• Hubs
• False positives