David Papo is based in the Center for Biomedical Technology at the Universidad Politécnica de Madrid, Spain. Together with Javier Buldú, Stefano Boccaletti and Edward Bullmore, he recently edited an issue for Philosophical Transactions B ‘Complex network theory and the brain’. We asked David a few questions about this topic and how the issue came together.
What is complex network theory?
Complex network theory is a modern statistical mechanics approach to graph theory, an almost three century old branch of applied mathematics. In its simplest form, a graph is a collection of nodes that can be connected to each other by means of links. Graph theory has traditionally been used to solve practical issues such as Leonhard Euler’s Königsberg bridge problem, or determining the maximum flow from source to sink in a pipe system.
When you look at real systems with thousands or millions of nodes (such as the internet), making sense of their structure can only be accomplished using statistical methods, which can explain macroscopic structure in terms of the interaction of a multitude of microscopic units. Complex network theory considers situations where the units are not an unstructured collection of points, but have relationships that are not random or regular, and is used to produce graphs that represent these relationships and patterns.
How is its application to neuroscience helping our understanding of the brain?
Network theory is particularly well equipped to describe general organizational principles of the brain. The brain can be represented as a collection of neurons (the ‘nodes’) connected by fibres (the ‘links’), and the same principle can be applied at larger scales when thinking about linked brain regions.
Coming up with a complete, meaningful account of such systems is a rather hard task, and may not be possible in many situations when using traditional modelling techniques. Complex network theory however provides a range of metrics through which important properties of brain anatomy and dynamics can become observable, and provides an elegant way of comparing structure and function, a fundamental issue for neuroscientists. Complex network theory also allows characterizing the balance between information processing efficiency and energetic consumption, and this in turn sheds light on how fundamental biological trade-offs are managed by the brain. It can also quantify properties such as robustness or vulnerability, and can therefore help understanding the impact of brain damage.
How did this theme issue come about and what are its major themes?
More than a decade has passed since the earliest applications of complex network theory to neuroscience, and the feeling is that in spite of some important achievements, complex network theory’s offers to neuroscience, arguably no major turning point has yet emerged as a result of its application.
In this theme issue, we wanted to crystallise the strengths, weaknesses, pitfalls and possible future avatars of complex network theory in neuroscience, in order to understand whether complex network theory will be an eternal promise or can possibly deliver. Original research and review articles provide a broad overview on some of the hottest theoretical, experimental and methodological topics in the field, from network reconstruction techniques, to the most recent graph theoretical methods for the description of brain anatomy and dynamics and its underlying constructive principles.
How is the field likely to develop in the future?
Network theory is likely to increase our ability to represent complex aspects such as the interplay between anatomical structure and brain dynamics, and to understand the forces that shaped the brain during the course of evolution. In addition, complex network theory will also help us classifying particular conditions, predicting future activity both at the fast scales of perception and at the very long ones of evolution, but also controlling brain activity, and steering it towards desired regimes. It could also be instrumental in understanding the brain’s ultimate potential, for instance it could help figuring out what is ‘learnable’ and what may not be.
Network theory in its current form was originally developed to describe systems, such as the internet, that differ in many fundamental ways from the brain. Fresh neuroscience-inspired network theory may be necessary for major developments in neuroscience to occur. This, in turn, may well be associated with the next turning point in the physics of complex networks.
‘Complex network theory and the brain’ published on Monday September 01 2014. More information can be found here.