Beware of the Small-World Neuroscientist!

Characterizing the brain's anatomical and dynamical organization and how this enables it to carry out complex tasks is highly non trivial. While there has long been strong evidence that brain anatomy can be thought of as a complex network at micro as well as macro scales, the use of functional imaging techniques has recently shown that brain dynamics also has a network-like structure.

Network Science (Newman, 2010) allows neuroscientists to quantify the general organizing principles of brain structure and dynamics at all scales in terms of highly reproducible, often universal properties shared by prima facie very different systems (Bullmore and Sporns, 2009). A network representation also helps addressing classical but complex issues such as structure-function relationships in a straightforward and elegant fashion, and determining how efficiently a system transfers information or how vulnerable it is to damage (Bullmore and Sporns, 2012; Papo et al., 2014).

One of the most studied global network properties is the small-world (SW) structure (Watts and Strogatz, 1998). In a SW network, nodes tend to form triangles, making the network locally robust. At the same time, the distance between any pair of nodes is much smaller than the network size and increases slowly (logarithmically) with the number of nodes in the network. This combination of properties has been suggested to represent a solution to the trade-off between module independence and specialization, and has been associated with optimal communication efficiency, high-speed and reliability of information transmission (Bullmore and Sporns, 2009, 2012).

In neuroscience, the SW structure has been reported for healthy brain anatomical and functional networks, and deviations from this global organization in various pathologies (Bassett et al., 2006; Stam, 2014). While there has been some heterogeneity in the adopted definition of SW network, these findings gave the neuroscience community hope that the SW could constitute a functionally meaningful universal feature of global brain organization.

In spite of this preliminary evidence, whether or not the brain is indeed a SW network is still very much an open question (Hilgetag and Goulas, 2015). The question that we address here is of a pragmatical rather than an ontological nature: independently of whether the brain is a SW network or not, to what extent can neuroscientists using standard system-level neuroimaging techniques interpret the SW construct in the context of functional brain networks?

In a typical experimental setting, neuroscientists record brain images, define nodes and links, construct a network, extract its topological properties, to finally assess their statistical significance and their possible functional meaning. We discuss evidence (some of which is already familiar to the neuroscience community) showing that behind each of these stages lurk fundamental technical, methodological or theoretical stumbling blocks that render the experimental quantification of the SW structure and its interpretation in terms of information processing problematic, questioning its usefulness as a descriptor of global brain organization. The emphasis is on functional brain activity reconstructed using standard system-level brain recording techniques, where the SW construct appears to be the most problematic.