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Why graph theory is important for the study of brain's structure? Why one should know about the graph theory for the learning about the structures and network of brain?

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  • $\begingroup$ but why one should bother about the graph theory why it is important for brain's structure and connectivity. That I am not getting $\endgroup$
    – Amanda
    Commented Feb 26, 2015 at 11:35
  • $\begingroup$ The language of graph theory can be useful for studying any network, including neural networks. $\endgroup$
    – user133281
    Commented Feb 26, 2015 at 11:55

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Brain neural networks can be represented as a network: nodes are neurons and edges are synapses. Like this, it's just a data structure.

This is already an oversimplification, since neurons connect to multiple other neurons through the same axon, so many graph-theoretic properties that arise are just artifacts of the data structure used.

Observations are made on the graph structure, e.g., degree distribution, and are used to compare competing random network models of the brain.

We can model brain behavior using random networks that behave similar to what's seen in biology. E.g. random networks can be studied rigorously using graph theory, but only very vague conclusions can be made for the real world, e.g., the "scale free" property of these networks contributes to their robustness (and reduces the likelihood of brain damage), and is thus evolutionary selected for.

Here's a fairly typical result in this area:

The functional resilience of brain networks to pathological attack can be modeled by deleting one or more nodes from the network and reestimating its small-world parameters. Deletion of any node might be expected to increase path length (reduce global efficiency), but deletion of hubs will have especially detrimental effects on overall network performance. Achard and colleagues (2006) measured path length of a brain functional network as it was degraded by random deletion of nodes and by targeted attack on the association cortical hubs. They found that the brain network was as resilient to random attack, and more resilient to targeted attack, than a comparable graph with a power law degree distribution (Fig. 6).

This suggests that the truncated power law degree distribution of brain networks, as well as possibly reflecting physical constraints on network growth, might also reflect a selection pressure favoring network topologies that are functionally resistant to local pathological attack.

--- Bassett, Bullmore, Small-world brain networks, Neuroscientist, 2006.

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