Graph Theory helps to map functional systems in brains
http://www.indiana.edu/~cortex/networks_nrn.pdf
Complex Brain Networks: graph theoretical analysis of structural and functional systems describes the different process of creating maps or graphs of neural networks and the implications of their findings. According to the article, each node of the network is viewed as neural area or a neuron and the edges are view as synaptic connections (the way neurons communicate with each other). Similar to the network graphs we studied in class, neural networks have high neural connectivity in clusters as well as local bridges. This leads me to hypothesize that the triadic closure property holds true in brains, due to the fact that neural areas/neurons are more likely to be linked to either a large number of common nodes. Being linked to just one node occurs far less often, just as local bridges are not as common. The local bridges, or long synaptic connections of the brain often connect two different areas or lobes of the brain, with different functions, so they also deliver more new and valuable information than the nodes with higher levels of connectivity do. The regions of high neuron connectivity seem to form modules, which have roles in similar functions. Furthermore, although structural (networks tied to the physical structure of the brain) and functional (networks based on which areas light up on fMRI scans) are different (can be seen as two different components), they are generally similar. An important step in brain mapping will be two see how the two different networks are connected and find the bridge/local bridges between them.
So far, large differences in neural networks are found among healthy individuals, those with Alzheimer’s Disease and those with schizophrenia. The neural networks in healthy people seem to be organized hierarchically, and as discussed above with high clustering and a lot of short paths. Those with Alzheimer’s have been found to have lower levels of local connectivity and clustering. This in turn increases the path length, hindering the efficiency of the networks. There is also an increase of global clustering. This I understood to mean there were more local bridges, and since there was a larger share of possibly unimportant information, there is more error in sending the right information. Schizophrenics’ neural networks differ because they often lack hierarchical structure. Connectivity and clustering becomes more random, instead of tightly linked sets of neurons.
Hopefully, as neurologists’ understanding of neural networks increases, their knowledge of psychiatric diseases will increase, as well as disorders such as autism, ADD and OCD. So far doctors have discovered that severing edges that link both hemispheres or certain lobes in the brain can eliminate seizures in epileptics. More research and understanding of these networks could lead to a discovery of new ways to manipulate networks, perhaps using theorems such as balanced networks or triadic closure property, in order to alleviate the symptoms of or cure these devastating diseases.