PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems
Many Parts, One Behaviour, Ch Networks as graphs: degree, distance and clustering
Problem
The human cerebral cortex contains about N=8.6×1010 neurons, and each neuron forms synaptic connections to roughly ⟨k⟩=7000 other neurons.
((a)) Using the tree estimate for the small-world effect, estimate the mean distance ℓ (in number of synaptic hops) between two randomly chosen neurons. State the assumption the estimate rests on.
((b)) Would you expect the true mean distance between cortical neurons to lie above or below this estimate? Give one reason, referring to a property of real networks discussed for the small-world effect.