  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. Due to limitations
of non-invasive 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: (i) remove uni-directional connections,
(ii) add reciprocal connections, and (iii) combine equal numbers of removed and
added uni-directional 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.
