Fig. 2: Applying repeatedly a random signal to nodes of the networks, we produced a disturbance that traveled in the system with a pace and amplitude that depended on the networks’ topology.
From: The small world coefficient 4.8 ± 1 optimizes information processing in 2D neuronal networks
To quantify the effect of small-world-ness on the information transported by the disturbance, we measured for each network topology (\({\rm{SW}}\)) the number of nodes reached by the signal (active nodes, a), and the total (\({I}_{{{\mathrm{grid}}}}/{I}_{{{\mathrm{input}}}}\), b) and the peak information (\({I}_{{{\mathrm{peak}}}}/{I}_{{{\mathrm{input}}}}\), c) in the network, compared to the same values associated to the initial stimulus. Then, we found how the number of active nodes (d), the normalized total (e), and peak information (f) behave relative to the values of these system’s variables determined for the special case \({\rm{SW}}=1\). The ratios reported in the insets d–f represent enhancement factors (\({\eta }^{{{\mathrm{nodes}}}}\), \({\eta }^{{{\mathrm{grid}}}}\), \({\eta }^{{{\mathrm{peak}}}}\)) and indicate how much the information flows in the network are enhanced due to the network topology. These diagrams were determined for a length and frequency of the initial stimulus of \(\triangle t=72\,{{\mathrm{ms}}}\) and \(f=133\,{{\mathrm{Hz}}}\).
