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. 2014 Feb 25;4:4184. doi: 10.1038/srep04184

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(A) (left): average normalized time to consensus vs. number of k-nearest neighbors in the topological distance for a statistically ample enough sample consisting of 1000 repeated dynamics; the associated standard deviations are shown through the errorbars. (B) (right): rate of variation of with k, , vs. k, obtained using the average normalized time to consensus. Five different swarm populations N are considered, namely N = 100, 300, 500, 1000 and 10000. The normalized time to consensus was calculated for each value of k in the range 3 to N − 1 although not all data points are shown here to ensure graph legibility. The quantity is numerically obtained using a 5-point stencil differentiation of order one³⁵. The consensus reaching threshold is ε = 10⁻⁴.

Inline graphic — (A) (left): average normalized time to consensus vs. number of k-nearest neighbors in the topological distance for a statistically ample enough sample consisting of 1000 repeated dynamics; the associated standard deviations are shown through the errorbars. (B) (right): rate of variation of with k, , vs. k, obtained using the average normalized time to consensus. Five different swarm populations N are considered, namely N = 100, 300, 500, 1000 and 10000. The normalized time to consensus was calculated for each value of k in the range 3 to N − 1 although not all data points are shown here to ensure graph legibility. The quantity is numerically obtained using a 5-point stencil differentiation of order one³⁵. The consensus reaching threshold is ε = 10⁻⁴.