Topology

Various aspects of the human brain have been investigated over the years. Of particular interest is the understanding of the topology of the brain networks. Once we know the baseline topology of the healthy human brain, we can start investigating differences between that baseline and patients suffering from disease.

Hubs

Networks can be assessed based on their degree distribution. If a small number of nodes in the network exist which have a relatively large degree (compared to the average of the network) the degree distribution exhibits a heavy-tail.

Example of a brain network

These nodes, so called hubs, have been of key interest while investigating brain networks. It has been shown that they are essential to the network architecture and the its function. More over they help define local segregation (specialisation) and global integration (efficient information transport) of the other nodes in the network.

Small-world

The small-world phenomenon has become an interesting research topic in the human brain. The human brain is likely to exhibit small-world characteristics, as it is a complex network on multiple levels and over time, supports segregated and distributed information processing and has most likely evolved to maximise efficiency while minimise wiring cost. In a study applying small-world topology to a neural network machine learning algorithm, it has also been shown that small-world networks allow for high rates of information processing and learning.

The existence of small-world topology in brain architecture has been first shown in 1998 by Watts and Strogatz for the structural networks of C. elegans. Following this discovery, brain networks of the cat, monkey and human have been investigated, both functionally and structurally, and it was shown that they exhibit this feature. Small-world architecture has also been of key interest when investigating injury and disease of the human brain.

Rich-club

In general the brain is thought to conserve wiring costs as an important selection criterion as to how and which connections to form. The existence of a rich-club, on the other hand is a high-cost architectural feature. This may seem surprising at first, however, the cost has to be offset against its cognitive value. Many studies have since investigated the consequences of a rich-club in the human brain and found that it is important not only for efficient information transport, but also for functional integration of nodes across the brain. It also seems that rich-club organisation is a general principle for brain networks and scientist have found it to exist in brain architectures of worms, cats, monkeys and humans.