The isoperimetric number or Cheeger constant is an indicator of the “bottleneckedness” of a network.
This measure is an NP measure and can only be calculated partially. It gives an estimation of the existence of a big enough group of nodes with too few connections to the rest of the network, meaning that this group of nodes will act as a bottleneck.
There is a curious relationship between the Isoperimetric number of a network A and the capacity to synchronize. This relationship is connected with a very interesting number that is associated with any network which is the algebraic connectivity which is the is the second-smallest eigenvalue of the Laplacian matrix of A. If this value is zero implies that the network is disconnected. The bigger it is this value the better will synchronize the network. Then, the interesting relationship is that ; where is the second smallest eigenvalue of the net Laplacian. Therefore a network that synchronize well will have a big meaning that will not have bottlenecks.
That seems to imply that a network with bottlenecks synchronize worst that one without them.
Our brain dedicates a big part of its volume to connect different parts of the cortex (white matter) and other different regions. The white matter made of axons seems to try to give a good connection opportunity to the neurons, reducing bottlenecks.