Figure 10.

Localized sub-sampling overestimates true small-world-ness. (A) Scheme of the simulation of the network topology. Neurons were placed in a 3D volume and linked with a distance-dependent wiring probability. Virtual electrodes were placed in the volume assuming that each electrode can pick up the neurons and their connections within a certain radius around the electrode tip. This represents the typical sampling geometry of multi-electrode recordings. (B) The distance-dependent probability was assumed to be a power-law with a constant baseline p(d) = p_o + kd^−a. The simulations were repeated for different exponents a. The distributions are shown here for a = 1, 2, and 3. The parameters were matched in each case to obtain the same average densities as found in the experiments for the two principal length scales (gray boxes). (C) The small-world-ness of the big network is shown as a function of the power-law exponent (black line). There is a small, but non-trivial small-world structure visible. The small-world-ness that is obtained by sub-sampling using a localized sampling scheme (“multi-electrode sampling,” red line) shows that the small-world-ness is generally overestimated, independent of the exact shape of the connectivity distribution. Random sub-sampling using the same degree of sparsity, however, has little effect on the estimate of small-world-ness (blue line).