We concur with Irimia and Van Horn that while much research is geared toward understanding the network features of brain regions (i.e., the nodes of the connectome), network properties of the edges between brain regions -representing white matter connections- may contain important additional information (van den Heuvel and Sporns, 2013b). The approach of Irimia and Van Horn to quantify how lesioning an individual connection affects the global network structure is an elegant way to shift focus from nodes to edges and provides insight in the role or importance of the disrupted connection (de Reus et al., in press).

In their paper, individual white matter edges were removed, one at a time, across reconstructed brain networks of 110 individuals. Brain networks were derived using diffusion tractography and comprised 165 regions. The effect of the removal of each edge was quantified by comparing four graph measures, being assortativity, characteristic path length, density and transitivity (see Rubinov and Sporns (2010) for an overview), before and after removal of the edge. Next, the observed differences with respect to these four metrics were combined into a single test statistic for each connection, expressing the significance of the effects caused by its removal. After evaluating the effects across all edges of the connectome, the authors found a diverse scaffold of white matter connections with a significant combined effect on the examined global network metrics, presenting (somewhat surprisingly) only little overlap with hub-to-hub rich club connections.

An essential ingredient of the proposed simulated lesioning approach are the network metrics chosen to assess the consequences of the simulated lesions. Unfortunately, it is generally difficult to judge which network metrics reflect “key” features of the brain and are suitable to capture lesion effects. For instance, since it is not always beneficial for a network to be assortative (Zhou et al., 2012), it is unclear whether changes in assortativity (e.g., due to lesions) are relevant for the functioning of brain networks.

In addition, there is a somewhat more attestable issue regarding the effectiveness of the mean shortest (i.e., characteristic) path length to assess changes upon connection lesioning. If the hypothesized disruption of a connection does eliminate some but not all shortest paths between two brain regions, the shortest path length between those regions does not change, while their mutual communication is still likely to be affected (Figure 1A). This issue is related to the observation by Rubinov and Sporns (2010) that “measures such as the characteristic path length… do not incorporate multiple and longer paths” and is especially relevant because of the high incidence of parallel processing paths in the brain (Goldman-Rakic, 1988; Alexander and Crutcher, 1990). A generalization of shortest path length that takes all possible paths between brain regions into account is the “communicability” metric of Estrada and Hatano (2008). This metric assigns higher weights to shorter paths (see the Supplementary Material for an explicit definition), which elegantly aligns with a recent report showing that shorter communication paths are associated with higher functional connectivity between brain regions (Goñi et al., 2014). Combined with some interesting applications of communicability in neuroscience (Duarte-Carvajalino et al., 2012; Mantzaris et al., 2013), especially as a tool to measure effects of actual (non-simulated) lesions in the brain (Crofts and Higham, 2009; Crofts et al., 2011), we believe that communicability may be a promising metric for simulated lesioning approaches.

To offer quantitative insight on this matter, we made a connectome map of the human cerebral cortex on the basis of high-quality diffusion-weighted MRI data from 215 subjects as provided by the Q3 data release of the Human Connectome Project (van Essen et al., 2012; Glasser et al., 2013). White matter fibers were traced using generalized q-sampling imaging (GQI; allowing for the reconstruction of crossing fibers) and streamline tractography (Yeh et al., 2010) and the cortex was parcellated into 219 distinct regions on the basis of a high-resolution subdivision of FreeSurfer's Desikan-Killiany atlas (Cammoun et al., 2012). Combining data from all 215 subjects, a group-averaged connectome map was formed by placing an edge between two brain regions if those regions were found to be connected in at least 60% of the subjects (de Reus and van den Heuvel, 2013b). Rich club regions were taken to include the 15% highest degree nodes of this connectome map (van den Heuvel et al., 2012).

The observed differences between simulated lesioning results assessed with characteristic path length, which is a conventional measure for communication and integration (Rubinov and Sporns, 2010), and simulated lesioning results assessed with Estrada's communicability or Tononi's integration metric, demonstrate that the answer to the question “which white matter connections cause large global-level effects when hypothetically lesioned?” largely depends on the metrics chosen to evaluate those effects, even if the metrics belong to the same “family.” This is further underscored by a post-hoc analysis in which we computed the impact of connection disruption on a measure for diffusion-based communication, estimating the number of steps needed to send a “signal” from one brain region to another under the assumption that the signal moves randomly along the connections of the network (see the Supplementary Material for details). Simulated lesioning outcomes with respect to this diffusion-based communication metric qualitatively differed from both characteristic path length and communicability outcomes, showing a “reverse” staircase with a low impact for rich club connections and a prominent role for local connections (Supplementary Figure 3).

Taken together, our results extend the observations of Irimia and Van Horn by showing that although hub-to-hub rich club connections may not appear in an aggregated lesioning scaffold derived using characteristic path length as communication metric, they do have a high impact on two other specific measures for communication and integration, namely Estrada's communicability and Tononi's integration metric. Rich club connections may thus not be critical for establishing (unique) short paths between remote brain regions, but do appear to play an important role in providing diverse communication paths across the network and integration of information between different functional domains. These observations nicely align with a growing number of reports suggesting that neural hubs and their connections play a central role in neural networks (van den Heuvel and Sporns, 2013b) and recent simulation studies suggesting that the presence of neural rich clubs enhances functional diversity (Senden et al., 2014).

The idea behind communicability that also parallel and longer paths may contribute to exchange of information between brain regions holds the middle between characteristic path length, assuming that signals only follow shortest paths, and diffusion-based metrics, assuming randomly moving signals [which actually tend to get “trapped” in densely connected zones such as the rich club (Rosvall and Bergstrom, 2008)]. In our opinion, this could be a plausible regime for the brain, especially because brain networks do not appear to be specifically optimized for either shortest path-based or diffusion-based communication (Goñi et al., 2013). An important future challenge in the field of connectomics will be to examine the biological relevance of such communication principles and other network measures, making it possible to determine which metrics encode “key” features of the brain's wiring architecture.